scholarly journals Interpolation and Model Checking for Nonlinear Arithmetic

2021 ◽  
pp. 266-288
Author(s):  
Dejan Jovanović ◽  
Bruno Dutertre
Keyword(s):  
Model Checking ◽  
Satisfiability Modulo Theories ◽  
Full Model ◽  
Model Checker ◽  
New Model ◽  
Smt Solver ◽  
Partial Model ◽  
Interpolation Procedure ◽  
State Of Art ◽  
Nonlinear Arithmetic

AbstractWe present a new model-based interpolation procedure for satisfiability modulo theories (SMT). The procedure uses a new mode of interaction with the SMT solver that we call solving modulo a model. This either extends a given partial model into a full model for a set of assertions or returns an explanation (a model interpolant) when no solution exists. This mode of interaction fits well into the model-constructing satisfiability (MCSAT) framework of SMT. We use it to develop an interpolation procedure for any MCSAT-supported theory. In particular, this method leads to an effective interpolation procedure for nonlinear real arithmetic. We evaluate the new procedure by integrating it into a model checker and comparing it with state-of-art model-checking tools for nonlinear arithmetic.

scholarly journals Model Checking Probabilistic Epistemic Logic for Probabilistic Multiagent Systems

2018 ◽  
Author(s):  
Chen Fu ◽  
Andrea Turrini ◽  
Xiaowei Huang ◽  
Lei Song ◽  
Yuan Feng ◽  
...  
Keyword(s):  
Linear Programming ◽  
Model Checking ◽  
Multiagent Systems ◽  
Epistemic Logic ◽  
Mixed Integer ◽  
Model Checker ◽  
Non Linear Programming ◽  
Smt Solver ◽  
Realistic Assumption ◽  
Novel Algorithm

In this work we study the model checking problem for probabilistic multiagent systems with respect to the probabilistic epistemic logic PETL, which can specify both temporal and epistemic properties. We show that under the realistic assumption of uniform schedulers, i.e., the choice of every agent depends only on its observation history, PETL model checking is undecidable. By restricting the class of schedulers to be memoryless schedulers, we show that the problem becomes decidable. More importantly, we design a novel algorithm which reduces the model checking problem into a mixed integer non-linear programming problem, which can then be solved by using an SMT solver. The algorithm has been implemented in an existing model checker and experiments are conducted on examples from the IPPC competitions.

scholarly journals Program Verification via Craig Interpolation for Presburger Arithmetic with Arrays

10.29007/zfkw ◽  
2018 ◽  
Author(s):  
Angelo Brillout ◽  
Daniel Kroening ◽  
Philipp Rümmer ◽  
Thomas Wahl
Keyword(s):  
Model Checking ◽  
Program Verification ◽  
Model Checker ◽  
Craig Interpolation ◽  
Presburger Arithmetic ◽  
C Programs ◽  
Full Theory ◽  
Software Model ◽  
Interpolation Procedure ◽  
Versatile Tool

Craig interpolation has become a versatile tool in formal verification, in particular for generating intermediate assertions in safety analysis and model checking. In this paper, we present a novel interpolation procedure for the theory of arrays, extending an interpolating calculus for the full theory of quantifier-free Presburger arithmetic, which will be presented at IJCAR this year. We investigate the use of this procedure in a software model checker for C programs. A distinguishing feature of the model checker is its ability to faithfully model machine arithmetic with an encoding into Presburger arithmetic with uninterpreted predicates. The interpolation procedure allows the synthesis of quantified invariants about arrays. This paper presents work in progress; we include initial experiments to demonstrate the potential of our method.

Engineering Theories with Z3

10.29007/x7b4 ◽  
2018 ◽  
Author(s):  
Nikolaj Bjorner
Keyword(s):  
Satisfiability Modulo Theories ◽  
Smt Solver ◽  
Testing Tools ◽  
Software And Hardware ◽  
Design And Testing

Modern Satisfiability Modulo Theories (SMT)solvers are fundamental to many programanalysis, verification, design and testing tools. They are a goodfit for the domain of software and hardware engineering becausethey support many domains that are commonly used by the tools.The meaning of domains are captured by theories that can beaxiomatized or supported by efficient <i>theory solvers</i>.Nevertheless, not all domains are handled by all solvers andmany domains and theories will never be native to any solver.We here explore different theories that extend MicrosoftResearch's SMT solver Z3's basicsupport. Some can be directly encoded or axiomatized,others make use of user theory plug-ins.Plug-ins are a powerful way for tools to supply their custom domains.

scholarly journals Verification and Strategy Synthesis for Coalition Announcement Logic

2021 ◽  
Author(s):  
Natasha Alechina ◽  
Hans van Ditmarsch ◽  
Rustam Galimullin ◽  
Tuo Wang
Keyword(s):  
Model Checking ◽  
Proof Of Concept ◽  
Model Checker ◽  
Complete Model ◽  
Concept Model ◽  
The Family ◽  
Winning Strategies ◽  
Epistemic Goals

AbstractCoalition announcement logic (CAL) is one of the family of the logics of quantified announcements. It allows us to reason about what a coalition of agents can achieve by making announcements in the setting where the anti-coalition may have an announcement of their own to preclude the former from reaching its epistemic goals. In this paper, we describe a PSPACE-complete model checking algorithm for CAL that produces winning strategies for coalitions. The algorithm is implemented in a proof-of-concept model checker.

scholarly journals Model Checking Temporal Epistemic Logic under Bounded Recall

2020 ◽  
Vol 34 (05) ◽  
pp. 7071-7078
Author(s):  
Francesco Belardinelli ◽  
Alessio Lomuscio ◽  
Emily Yu
Keyword(s):  
Model Checking ◽  
Incomplete Information ◽  
Epistemic Logic ◽  
Upper Bounds ◽  
Experimental Results ◽  
Model Checker ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Bounded Recall

We study the problem of verifying multi-agent systems under the assumption of bounded recall. We introduce the logic CTLKBR, a bounded-recall variant of the temporal-epistemic logic CTLK. We define and study the model checking problem against CTLK specifications under incomplete information and bounded recall and present complexity upper bounds. We present an extension of the BDD-based model checker MCMAS implementing model checking under bounded recall semantics and discuss the experimental results obtained.

scholarly journals Scheduling Optimization of Time-Triggered Cyber-Physical Systems Based on Fuzzy-Controlled QPSO and SMT Solver

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 668
Author(s):  
Jie Jian ◽  
Lide Wang ◽  
Huang Chen ◽  
Xiaobo Nie
Keyword(s):  
Scheduling Algorithm ◽  
Cyber Physical Systems ◽  
Satisfiability Modulo Theories ◽  
Random Mutation ◽  
Physical Systems ◽  
Smt Solver ◽  
Time Requirements ◽  
Adaptive Adjustment ◽  
Periodic Traffic ◽  
Cost Efficient

The time-triggered communication paradigm is a cost-efficient way to meet the real-time requirements of cyber-physical systems. It is a non-deterministic polynomial NP-complete problem for multi-hop networks and non-strictly periodic traffic. A two-level scheduling approach is proposed to simplify the complexity during optimization. In the first level, a fuzzy-controlled quantum-behaved particle swarm optimization (FQPSO) algorithm is proposed to optimize the scheduling performance by assigning time-triggered frame instances to the basic periods of each link. In order to prevent population from high aggregation, a random mutation mechanism is used to disturb particles at the aggregation point and enhance the diversity at later stages. Fuzzy logic is introduced and well designed to realize a dynamic adaptive adjustment of the contraction–expansion coefficient and mutation rate in FQPSO. In the second level, we use an improved Satisfiability Modulo Theories (SMT) scheduling algorithm to solve the collision-free and temporal constraints. A schedulability ranking method is proposed to accelerate the computation of the SMT-based incremental scheduler. Our approach can co-optimize the jitter and load balance of communication for an off-line schedule. The experiments show that the proposed approach can improve the performance of the scheduling table, reduce the optimization time, and reserve space for incremental messages.

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