Rich Counter-Examples for Temporal-Epistemic Logic Model Checking

Model checking verifies that a model of a system satisfies a given property, and otherwise produces a counter-example explaining the violation. The verified properties are formally expressed in temporal logics. Some temporal logics, such as CTL, are branching: they allow to express facts about the whole computation tree of the model, rather than on each single linear computation. This branching aspect is even more critical when dealing with multi-modal logics, i.e. logics expressing facts about systems with several transition relations. A prominent example is CTLK, a logic that reasons about temporal and epistemic properties of multi-agent systems. In general, model checkers produce linear counter-examples for failed properties, composed of a single computation path of the model. But some branching properties are only poorly and partially explained by a linear counter-example. This paper proposes richer counter-example structures called tree-like annotated counter-examples (TLACEs), for properties in Action-Restricted CTL (ARCTL), an extension of CTL quantifying paths restricted in terms of actions labeling transitions of the model. These counter-examples have a branching structure that supports more complete description of property violations. Elements of these counter-examples are annotated with parts of the property to give a better understanding of their structure. Visualization and browsing of these richer counter-examples become a critical issue, as the number of branches and states can grow exponentially for deeply-nested properties. This paper formally defines the structure of TLACEs, characterizes adequate counter-examples w.r.t. models and failed properties, and gives a generation algorithm for ARCTL properties. It also illustrates the approach with examples in CTLK, using a reduction of CTLK to ARCTL. The proposed approach has been implemented, first by extending the NuSMV model checker to generate and export branching counter-examples, secondly by providing an interactive graphical interface to visualize and browse them.Comment: In Proceedings IWIGP 2012, arXiv:1202.422

MCMAS-SLK: A Model Checker for the Verification of Strategy Logic Specifications

We introduce MCMAS-SLK, a BDD-based model checker for the verification of systems against specifications expressed in a novel, epistemic variant of strategy logic. We give syntax and semantics of the specification language and introduce a labelling algorithm for epistemic and strategy logic modalities. We provide details of the checker which can also be used for synthesising agents' strategies so that a specification is satisfied by the system. We evaluate the efficiency of the implementation by discussing the results obtained for the dining cryptographers protocol and a variant of the cake-cutting problem

Comparing BDD and SAT based techniques for model checking Chaum's Dining Cryptographers Protocol

We analyse different versions of the Dining Cryptographers protocol by means of automatic verification via model checking. Specifically we model the protocol in terms of a network of communicating automata and verify that the protocol meets the anonymity requirements specified. Two different model checking techniques (ordered binary decision diagrams and SAT-based bounded model checking) are evaluated and compared to verify the protocols

Automated Verification of Quantum Protocols using MCMAS

We present a methodology for the automated verification of quantum protocols using MCMAS, a symbolic model checker for multi-agent systems The method is based on the logical framework developed by D'Hondt and Panangaden for investigating epistemic and temporal properties, built on the model for Distributed Measurement-based Quantum Computation (DMC), an extension of the Measurement Calculus to distributed quantum systems. We describe the translation map from DMC to interpreted systems, the typical formalism for reasoning about time and knowledge in multi-agent systems. Then, we introduce dmc2ispl, a compiler into the input language of the MCMAS model checker. We demonstrate the technique by verifying the Quantum Teleportation Protocol, and discuss the performance of the tool.Comment: In Proceedings QAPL 2012, arXiv:1207.055

Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables

We show that Branching-time temporal logics CTL and CTL*, as well as Alternating-time temporal logics ATL and ATL*, are as semantically expressive in the language with a single propositional variable as they are in the full language, i.e., with an unlimited supply of propositional variables. It follows that satisfiability for CTL, as well as for ATL, with a single variable is EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a single variable is 2EXPTIME-complete,--i.e., for these logics, the satisfiability for formulas with only one variable is as hard as satisfiability for arbitrary formulas.Comment: Prefinal version of the published pape

Model-Checking an Alternating-time Temporal Logic with Knowledge, Imperfect Information, Perfect Recall and Communicating Coalitions

We present a variant of ATL with distributed knowledge operators based on a synchronous and perfect recall semantics. The coalition modalities in this logic are based on partial observation of the full history, and incorporate a form of cooperation between members of the coalition in which agents issue their actions based on the distributed knowledge, for that coalition, of the system history. We show that model-checking is decidable for this logic. The technique utilizes two variants of games with imperfect information and partially observable objectives, as well as a subset construction for identifying states whose histories are indistinguishable to the considered coalition