Bounded Reachability for Temporal Logic over Constraint Systems

We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such logic can be undecidable. We introduce suitable restrictions and assumptions that are shown to make the satisfiability problem for the extended logic decidable. Moreover for a large class of constraint systems we propose an encoding that realize an effective decision procedure for the Bounded Reachability problem

ATLsc with partial observation

Alternating-time temporal logic with strategy contexts (ATLsc) is a powerful formalism for expressing properties of multi-agent systems: it extends CTL with strategy quantifiers, offering a convenient way of expressing both collaboration and antagonism between several agents. Incomplete observation of the state space is a desirable feature in such a framework, but it quickly leads to undecidable verification problems. In this paper, we prove that uniform incomplete observation (where all players have the same observation) preserves decidability of the model-checking problem, even for very expressive logics such as ATLsc.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

From Quantified CTL to QBF

QCTL extends the temporal logic CTL with quantifications over atomic propositions. This extension is known to be very expressive: QCTL allows us to express complex properties over Kripke structures (it is as expressive as MSO). Several semantics exist for the quantifications: here, we work with the structure semantics, where the extra propositions label the Kripke structure (and not its execution tree), and the model-checking problem is known to be PSPACE-complete in this framework. We propose a model-checking algorithm for QCTL based on a reduction to QBF. We consider several reduction strategies, and we compare them with a prototype (based on the SMT-solver Z3) on several examples

Linear Encodings of Bounded LTL Model Checking

We consider the problem of bounded model checking (BMC) for linear temporal logic (LTL). We present several efficient encodings that have size linear in the bound. Furthermore, we show how the encodings can be extended to LTL with past operators (PLTL). The generalised encoding is still of linear size, but cannot detect minimal length counterexamples. By using the virtual unrolling technique minimal length counterexamples can be captured, however, the size of the encoding is quadratic in the specification. We also extend virtual unrolling to Buchi automata, enabling them to accept minimal length counterexamples. Our BMC encodings can be made incremental in order to benefit from incremental SAT technology. With fairly small modifications the incremental encoding can be further enhanced with a termination check, allowing us to prove properties with BMC. Experiments clearly show that our new encodings improve performance of BMC considerably, particularly in the case of the incremental encoding, and that they are very competitive for finding bugs. An analysis of the liveness-to-safety transformation reveals many similarities to the BMC encodings in this paper. Using the liveness-to-safety translation with BDD-based invariant checking results in an efficient method to find shortest counterexamples that complements the BMC-based approach.Comment: Final version for Logical Methods in Computer Science CAV 2005 special issu

Discounting in LTL

In recent years, there is growing need and interest in formalizing and reasoning about the quality of software and hardware systems. As opposed to traditional verification, where one handles the question of whether a system satisfies, or not, a given specification, reasoning about quality addresses the question of \emph{how well} the system satisfies the specification. One direction in this effort is to refine the "eventually" operators of temporal logic to {\em discounting operators}: the satisfaction value of a specification is a value in $[0,1]$, where the longer it takes to fulfill eventuality requirements, the smaller the satisfaction value is. In this paper we introduce an augmentation by discounting of Linear Temporal Logic (LTL), and study it, as well as its combination with propositional quality operators. We show that one can augment LTL with an arbitrary set of discounting functions, while preserving the decidability of the model-checking problem. Further augmenting the logic with unary propositional quality operators preserves decidability, whereas adding an average-operator makes some problems undecidable. We also discuss the complexity of the problem, as well as various extensions

Satisfiability of CTL* with constraints

We show that satisfiability for CTL* with equality-, order-, and modulo-constraints over Z is decidable. Previously, decidability was only known for certain fragments of CTL*, e.g., the existential and positive fragments and EF.Comment: To appear at Concur 201