737 lines
24 KiB
Python
737 lines
24 KiB
Python
"""
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SMT-based Model Checking Module for RS with Concentrations and Context Automaton
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"""
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from z3 import *
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from time import time
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from sys import stdout
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from itertools import chain
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import resource
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from colour import *
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from logics import rsLTL_Encoder
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# def simplify(x):
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# return x
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class SmtCheckerRSC(object):
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def __init__(self, rsca):
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rsca.sanity_check()
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if not rsca.is_with_concentrations():
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raise RuntimeError("RS and CA with concentrations expected")
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self.rs = rsca.rs
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self.ca = rsca.ca
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self.initialise()
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def initialise(self):
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"""Initialises all the variables used by the checker"""
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self.v = []
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self.v_ctx = []
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self.ca_state = []
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self.next_level_to_encode = 0
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self.loop_position = Int("loop_position")
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self.solver = Solver() # For("QF_FD")
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self.verification_time = None
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def reset(self):
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"""Reinitialises the state of the checker"""
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self.initialise()
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def prepare_all_variables(self):
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"""Encodes all the variables"""
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self.prepare_state_variables()
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self.prepare_context_variables()
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self.next_level_to_encode += 1
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def prepare_context_variables(self):
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"""Encodes all the context variables"""
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level = self.next_level_to_encode
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variables = []
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for entity in self.rs.background_set:
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variables.append(Int("C" + str(level) + "_" + entity))
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self.v_ctx.append(variables)
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def prepare_state_variables(self):
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"""Encodes all the state variables"""
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level = self.next_level_to_encode
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variables = []
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for entity in self.rs.background_set:
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variables.append(Int("L" + str(level) + "_" + entity))
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self.v.append(variables)
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self.ca_state.append(Int("CA" + str(level) + "_state"))
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def enc_concentration_levels_assertion(self, level):
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"""Encodes assertions that (some) variables need to be >0
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We do not need to actually control all the variables,
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only those that can possibly go below 0.
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"""
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enc_nz = True
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for e_i in range(len(self.rs.background_set)):
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v = self.v[level][e_i]
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v_ctx = self.v_ctx[level][e_i]
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e_max = self.rs.get_max_concentration_level(e_i)
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enc_nz = simplify(
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And(enc_nz, v >= 0, v_ctx >= 0, v <= e_max, v_ctx <= e_max)
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)
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return enc_nz
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def enc_init_state(self, level):
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"""Encodes the initial state at the given level"""
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rs_init_state_enc = True
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for v in self.v[level]:
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# the initial concentration levels are zeroed
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rs_init_state_enc = simplify(And(rs_init_state_enc, v == 0))
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ca_init_state_enc = self.ca_state[level] == self.ca.get_init_state_id()
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init_state_enc = simplify(And(rs_init_state_enc, ca_init_state_enc))
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return init_state_enc
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def enc_produced_concentration(self, level, prod_entity):
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"""Encodes the produced concentrations for the given level and entity"""
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rcts_for_prod_entity = []
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if prod_entity in self.rs.get_reactions_by_product():
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rcts_for_prod_entity = self.rs.get_reactions_by_product()[prod_entity]
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meta_reactions = []
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if prod_entity in self.rs.meta_reactions:
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meta_reactions = self.rs.meta_reactions[prod_entity]
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permanency_inhibition = None
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if prod_entity in self.rs.permanent_entities:
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permanency_inhibition = self.rs.permanent_entities[prod_entity]
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if rcts_for_prod_entity == [] and meta_reactions == []:
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# this should never happen
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return simplify(self.v[level + 1][prod_entity] == 0)
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enc_enabledness = False
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# ----------- ordinary reactions --------------------------------------------
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enc_rct_prod = False
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enc_ordinary_reactions_enabledness = False
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for reactants, inhibitors, products in rcts_for_prod_entity:
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enc_reactants = True
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for reactant, concentration in reactants:
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enc_reactants = simplify(
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And(
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enc_reactants,
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Or(
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self.v[level][reactant] >= concentration,
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self.v_ctx[level][reactant] >= concentration,
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),
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)
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)
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enc_inhibitors = True
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for inhibitor, concentration in inhibitors:
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enc_inhibitors = simplify(
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And(
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enc_inhibitors,
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And(
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self.v[level][inhibitor] < concentration,
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self.v_ctx[level][inhibitor] < concentration,
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),
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)
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)
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enc_rct_enabled = And(enc_reactants, enc_inhibitors)
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enc_products = self.v[level + 1][products[0][0]] == products[0][1]
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enc_rct_prod = simplify(If(enc_rct_enabled, enc_products, enc_rct_prod))
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enc_enabledness = simplify(Or(enc_enabledness, enc_rct_enabled))
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enc_ordinary_reactions_enabledness = simplify(
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Or(enc_ordinary_reactions_enabledness, enc_rct_enabled)
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)
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# -------- meta reactions ---------------------------------------------------
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for r_type, command_entity, reactants, inhibitors in meta_reactions:
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# command entity is e.g. 'inc' for incrementation operation
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# (inc,W) gives us the value W by which the given entity's value should be incremented
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enc_reactants = True
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enc_inhibitors = True
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for reactant, concentration in reactants:
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enc_reactants = simplify(
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And(
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enc_reactants,
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Or(
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self.v[level][reactant] >= concentration,
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self.v_ctx[level][reactant] >= concentration,
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),
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)
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)
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# command entity needs to be present (with concentration level > 0) in order to perform the operation
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enc_reactants = simplify(
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And(
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enc_reactants,
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Or(
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self.v[level][command_entity] > 0,
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self.v_ctx[level][command_entity] > 0,
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),
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)
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)
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for inhibitor, concentration in inhibitors:
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enc_inhibitors = simplify(
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And(
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enc_inhibitors,
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And(
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self.v[level][inhibitor] < concentration,
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self.v_ctx[level][inhibitor] < concentration,
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),
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)
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)
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if r_type == "inc":
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value_after_inc = If(
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self.v[level][prod_entity] > self.v_ctx[level][prod_entity],
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self.v[level][prod_entity],
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self.v_ctx[level][prod_entity],
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) + If(
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self.v[level][command_entity] > self.v_ctx[level][command_entity],
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self.v[level][command_entity],
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self.v_ctx[level][command_entity],
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)
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enc_products = self.v[level + 1][prod_entity] == value_after_inc
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elif r_type == "dec":
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value_after_dec = simplify(
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If(
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self.v[level][prod_entity] > self.v_ctx[level][prod_entity],
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self.v[level][prod_entity],
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self.v_ctx[level][prod_entity],
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)
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- If(
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self.v[level][command_entity]
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> self.v_ctx[level][command_entity],
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self.v[level][command_entity],
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self.v_ctx[level][command_entity],
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)
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)
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enc_products = self.v[level + 1][prod_entity] == If(
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value_after_dec < 0, 0, value_after_dec
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)
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else:
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raise RuntimeError("Unknown meta-reaction type: " + repr(r_type))
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enc_meta_reaction_enabledness = And(
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enc_reactants, enc_inhibitors, Not(enc_ordinary_reactions_enabledness)
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)
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enc_enabledness = simplify(
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Or(enc_enabledness, enc_meta_reaction_enabledness)
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)
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enc_rct_prod = simplify(
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Or(enc_rct_prod, And(enc_meta_reaction_enabledness, enc_products))
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)
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# -----------------------------------------------------------------------------
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if not permanency_inhibition == None:
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enc_reactants = Or(
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self.v[level][prod_entity] >= concentration,
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self.v_ctx[level][prod_entity] >= concentration,
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)
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enc_inhibitors = True
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for inhibitor, concentration in permanency_inhibition:
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enc_inhibitors = simplify(
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And(
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enc_inhibitors,
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And(
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self.v[level][inhibitor] < concentration,
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self.v_ctx[level][inhibitor] < concentration,
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),
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)
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)
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enc_products = simplify(
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self.v[level + 1][prod_entity]
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== If(
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self.v[level][prod_entity] > self.v_ctx[level][prod_entity],
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self.v[level][prod_entity],
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self.v_ctx[level][prod_entity],
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)
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)
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enc_permanency_enabledness = And(
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enc_reactants, enc_inhibitors, Not(enc_ordinary_reactions_enabledness)
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)
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enc_enabledness = simplify(Or(enc_enabledness, enc_permanency_enabledness))
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enc_permanency = And(enc_permanency_enabledness, enc_products)
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enc_rct_prod = simplify(Or(enc_rct_prod, enc_permanency))
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# -----------------------------------------------------------------------------
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enc_when_to_produce_zero_conc = simplify(
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And(Not(enc_enabledness), self.v[level + 1][prod_entity] == 0)
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)
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enc_rct_prod = Or(enc_rct_prod, enc_when_to_produce_zero_conc)
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return enc_rct_prod
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def enc_transition_relation(self, level):
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return simplify(And(self.enc_rs_trans(level), self.enc_automaton_trans(level)))
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def enc_rs_trans(self, level):
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"""Encodes the transition relation"""
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unused_entities = set(range(len(self.rs.background_set)))
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enc_trans = True
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reactions = self.rs.get_reactions_by_product()
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meta_reactions = self.rs.meta_reactions
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for prod_entity in chain(reactions, meta_reactions):
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unused_entities.discard(prod_entity)
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enc_trans = simplify(
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And(enc_trans, self.enc_produced_concentration(level, prod_entity))
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)
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for prod_entity in unused_entities:
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enc_trans = simplify(And(enc_trans, self.v[level + 1][prod_entity] == 0))
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return enc_trans
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def enc_automaton_trans(self, level):
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"""Encodes the transition relation for the context automaton"""
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enc_trans = False
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for src, ctx, dst in self.ca.transitions:
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src_enc = self.ca_state[level] == src
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dst_enc = self.ca_state[level + 1] == dst
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all_ent = set(range(len(self.rs.background_set)))
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incl_ctx = set([e for e, c in ctx])
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excl_ctx = all_ent - incl_ctx
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ctx_enc = True
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for e, c in ctx:
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ctx_enc = simplify(And(ctx_enc, self.v_ctx[level][e] == c))
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for e in excl_ctx:
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ctx_enc = simplify(And(ctx_enc, self.v_ctx[level][e] == 0))
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cur_trans = simplify(And(src_enc, ctx_enc, dst_enc))
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enc_trans = simplify(Or(enc_trans, cur_trans))
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return enc_trans
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def enc_exact_state(self, level, state):
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"""Encodes the state at the given level with the exact concentration values"""
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raise RuntimeError("Should not be used with RSC")
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def enc_min_state(self, level, state):
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"""Encodes the state at the given level with the minimal required concentration levels"""
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enc = True
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for ent, conc in state:
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e_id = self.rs.get_entity_id(ent)
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enc = And(enc, self.v[level][e_id] >= conc)
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return simplify(enc)
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def enc_state_with_blocking(self, level, prop):
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"""Encodes the state at the given level with blocking certain concentrations"""
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required, blocked = prop
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enc = True
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for ent, conc in required:
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e_id = self.rs.get_entity_id(ent)
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enc = And(enc, self.v[level][e_id] >= conc)
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for ent, conc in blocked:
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e_id = self.rs.get_entity_id(ent)
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enc = And(enc, self.v[level][e_id] < conc)
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return simplify(enc)
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def decode_witness(self, max_level, print_model=False):
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m = self.solver.model()
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if print_model:
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print(m)
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for level in range(max_level + 1):
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print("\n{: >70}".format("[ level=" + repr(level) + " ]"))
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print(" State: {", end=""),
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for var_id in range(len(self.v[level])):
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var_rep = repr(m[self.v[level][var_id]])
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if not var_rep.isdigit():
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raise RuntimeError(
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"unexpected: representation is not a positive integer"
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)
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if int(var_rep) > 0:
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print(" " + self.rs.get_entity_name(var_id) + "=" + var_rep, end="")
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# print(" " + repr(m[self.v[level][var_id]]), end="")
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print(" }")
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if level != max_level:
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print(" Context set: ", end="")
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print("{", end="")
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for var_id in range(len(self.v[level])):
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var_rep = repr(m[self.v_ctx[level][var_id]])
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if not var_rep.isdigit():
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raise RuntimeError(
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"unexpected: representation is not a positive integer"
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)
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if int(var_rep) > 0:
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print(
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" " + self.rs.get_entity_name(var_id) + "=" + var_rep,
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end="",
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)
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print(" }")
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def check_rsltl(
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self,
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formula,
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print_witness=True,
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print_time=True,
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print_mem=True,
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max_level=None,
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):
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"""Bounded Model Checking for rsLTL properties"""
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self.reset()
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print("[" + colour_str(C_BOLD, "i") + "] Running rsLTL bounded model checking")
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print("[" + colour_str(C_BOLD, "i") + "] Formula: " + str(formula))
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if print_time:
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# start = time()
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start = resource.getrusage(resource.RUSAGE_SELF).ru_utime
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self.prepare_all_variables()
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self.solver.add(self.enc_init_state(0))
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self.current_level = 0
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self.prepare_all_variables()
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self.solver.add(self.enc_concentration_levels_assertion(0))
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encoder = rsLTL_Encoder(self)
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encoder.load_variables(
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var_rs=self.v, var_ctx=self.v_ctx, var_loop_pos=self.loop_position
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)
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while True:
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self.prepare_all_variables()
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self.solver.add(
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self.enc_concentration_levels_assertion(self.current_level + 1)
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)
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print(
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"\n{:-^70}".format(
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"[ Working at level=" + str(self.current_level) + " ]"
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)
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)
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stdout.flush()
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# reachability test:
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self.solver.push()
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print(
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"[" + colour_str(C_BOLD, "i") + "] Generating the formula encoding..."
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)
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f = encoder.get_encoding(formula, self.current_level)
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ncalls = encoder.get_ncalls()
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print(
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"["
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+ colour_str(C_BOLD, "i")
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+ "] Cache hits: "
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+ str(encoder.get_cache_hits())
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+ ", encode calls: "
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+ str(ncalls[0])
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+ " (approx: "
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+ str(ncalls[1])
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+ ")"
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)
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print(
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"[" + colour_str(C_BOLD, "i") + "] Adding the formula to the solver..."
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)
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encoder.flush_cache()
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self.solver.add(f)
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print("[" + colour_str(C_BOLD, "i") + "] Adding the loops encoding...")
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self.solver.add(self.get_loop_encodings())
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result = self.solver.check()
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if result == sat:
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print(
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"["
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+ colour_str(C_BOLD, "+")
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+ "] "
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+ colour_str(C_GREEN, "SAT at level=" + str(self.current_level))
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)
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if print_witness:
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print("\n{:=^70}".format("[ WITNESS ]"))
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self.decode_witness(self.current_level)
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break
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else:
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self.solver.pop()
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print("[" + colour_str(C_BOLD, "i") + "] Unrolling the transition relation")
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self.solver.add(self.enc_transition_relation(self.current_level))
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print("{:->70}".format("[ level=" + str(self.current_level) + " done ]"))
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self.current_level += 1
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if not max_level is None and self.current_level > max_level:
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print("Stopping at level=" + str(max_level))
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break
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if print_time:
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# stop = time()
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stop = resource.getrusage(resource.RUSAGE_SELF).ru_utime
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self.verification_time = stop - start
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print()
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print(
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"\n[i] {: >60}".format(" Time: " + repr(self.verification_time) + " s")
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)
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if print_mem:
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print(
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"[i] {: >60}".format(
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" Memory: "
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+ repr(
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|
resource.getrusage(resource.RUSAGE_SELF).ru_maxrss
|
|
/ (1024 * 1024)
|
|
)
|
|
+ " MB"
|
|
)
|
|
)
|
|
|
|
def dummy_unroll(self, levels):
|
|
"""Unrolls the variables for testing purposes"""
|
|
|
|
self.current_level = -1
|
|
for i in range(levels + 1):
|
|
self.prepare_all_variables()
|
|
self.current_level += 1
|
|
|
|
print(C_MARK_INFO + " Dummy Unrolling done.")
|
|
|
|
def state_equality(self, level_A, level_B):
|
|
"""Encodes equality of two states at two different levels"""
|
|
|
|
eq_enc = True
|
|
|
|
for e_i in range(len(self.rs.background_set)):
|
|
e_i_equality = self.v[level_A][e_i] == self.v[level_B][e_i]
|
|
eq_enc = simplify(And(eq_enc, e_i_equality))
|
|
|
|
eq_enc_ctxaut = self.ca_state[level_A] == self.ca_state[level_B]
|
|
eq_enc = simplify(And(eq_enc, eq_enc_ctxaut))
|
|
|
|
return eq_enc
|
|
|
|
def get_loop_encodings(self):
|
|
k = self.current_level
|
|
loop_var = self.loop_position
|
|
|
|
loop_enc = True
|
|
|
|
"""
|
|
(loop_var == i) means that there is a loop taking back to the state (i-1)
|
|
|
|
Therefore, the encoding starts at 1, not at 0.
|
|
"""
|
|
|
|
for i in range(1, k + 1):
|
|
loop_enc = simplify(
|
|
And(loop_enc, Implies(loop_var == i, self.state_equality(i - 1, k)))
|
|
)
|
|
|
|
return loop_enc
|
|
|
|
def check_reachability(
|
|
self, state, print_witness=True, print_time=True, print_mem=True, max_level=1000
|
|
):
|
|
"""Main testing function"""
|
|
|
|
self.reset()
|
|
|
|
if print_time:
|
|
# start = time()
|
|
start = resource.getrusage(resource.RUSAGE_SELF).ru_utime
|
|
|
|
self.prepare_all_variables()
|
|
self.solver.add(self.enc_init_state(0))
|
|
self.current_level = 0
|
|
|
|
self.prepare_all_variables()
|
|
|
|
self.solver.add(self.enc_concentration_levels_assertion(0))
|
|
|
|
while True:
|
|
self.prepare_all_variables()
|
|
self.solver.add(
|
|
self.enc_concentration_levels_assertion(self.current_level + 1)
|
|
)
|
|
|
|
print(
|
|
"\n{:-^70}".format(
|
|
"[ Working at level=" + str(self.current_level) + " ]"
|
|
)
|
|
)
|
|
stdout.flush()
|
|
|
|
# reachability test:
|
|
print("[" + colour_str(C_BOLD, "i") + "] Adding the reachability test...")
|
|
self.solver.push()
|
|
|
|
self.solver.add(self.enc_state_with_blocking(self.current_level, state))
|
|
|
|
result = self.solver.check()
|
|
if result == sat:
|
|
print(
|
|
"["
|
|
+ colour_str(C_BOLD, "+")
|
|
+ "] "
|
|
+ colour_str(C_GREEN, "SAT at level=" + str(self.current_level))
|
|
)
|
|
if print_witness:
|
|
print("\n{:=^70}".format("[ WITNESS ]"))
|
|
self.decode_witness(self.current_level)
|
|
break
|
|
else:
|
|
self.solver.pop()
|
|
|
|
print("[" + colour_str(C_BOLD, "i") + "] Unrolling the transition relation")
|
|
self.solver.add(self.enc_transition_relation(self.current_level))
|
|
|
|
print("{:->70}".format("[ level=" + str(self.current_level) + " done ]"))
|
|
self.current_level += 1
|
|
|
|
if self.current_level > max_level:
|
|
print("Stopping at level=" + str(max_level))
|
|
break
|
|
|
|
if print_time:
|
|
# stop = time()
|
|
stop = resource.getrusage(resource.RUSAGE_SELF).ru_utime
|
|
self.verification_time = stop - start
|
|
print()
|
|
print(
|
|
"\n[i] {: >60}".format(" Time: " + repr(self.verification_time) + " s")
|
|
)
|
|
|
|
if print_mem:
|
|
print(
|
|
"[i] {: >60}".format(
|
|
" Memory: "
|
|
+ repr(
|
|
resource.getrusage(resource.RUSAGE_SELF).ru_maxrss
|
|
/ (1024 * 1024)
|
|
)
|
|
+ " MB"
|
|
)
|
|
)
|
|
|
|
def get_verification_time(self):
|
|
return self.verification_time
|
|
|
|
def show_encoding(
|
|
self,
|
|
state,
|
|
print_witness=True,
|
|
print_time=False,
|
|
print_mem=False,
|
|
max_level=100,
|
|
):
|
|
"""Encoding debug function"""
|
|
|
|
self.reset()
|
|
|
|
self.prepare_all_variables()
|
|
init_s = self.enc_init_state(0)
|
|
print(init_s)
|
|
self.solver.add(init_s)
|
|
self.current_level = 0
|
|
|
|
self.prepare_all_variables()
|
|
|
|
while True:
|
|
self.prepare_all_variables()
|
|
|
|
print("-----[ Working at level=" + str(self.current_level) + " ]-----")
|
|
stdout.flush()
|
|
|
|
# reachability test:
|
|
print("[i] Adding the reachability test...")
|
|
self.solver.push()
|
|
|
|
s = self.enc_min_state(self.current_level, state)
|
|
print("Test: ", s)
|
|
|
|
self.solver.add(s)
|
|
|
|
result = self.solver.check()
|
|
if result == sat:
|
|
print(
|
|
"\n[+] "
|
|
+ colour_str(C_RED, "SAT at level=" + str(self.current_level))
|
|
)
|
|
if print_witness:
|
|
self.decode_witness(self.current_level)
|
|
break
|
|
else:
|
|
self.solver.pop()
|
|
|
|
print("[i] Unrolling the transition relation")
|
|
t = self.enc_transition_relation(self.current_level)
|
|
print(t)
|
|
self.solver.add(t)
|
|
|
|
print("-----[ level=" + str(self.current_level) + " done ]")
|
|
self.current_level += 1
|
|
|
|
if self.current_level > max_level:
|
|
print("Stopping at level=" + str(max_level))
|
|
break
|
|
else:
|
|
x = input("Next level? ")
|
|
x = x.lower()
|
|
if not (x == "y" or x == "yes"):
|
|
break
|