Uniform approaches to the verification of finite state systems (original) (raw)

On decidability of LTL model checking for process rewrite systems

Acta Informatica, 2009

We establish a decidability boundary of the model checking problem for infinitestate systems defined by Process Rewrite Systems (PRS) or weakly extended Process Rewrite Systems (wPRS), and properties described by basic fragments of action-based Linear Temporal Logic (LTL) with both future and past operators. It is known that the problem for general LTL properties is decidable for Petri nets and for pushdown processes, while it is undecidable for PA processes. We show that the problem is decidable for wPRS if we consider properties defined by LTL formulae with only modalities strict eventually, strict always, and their past counterparts. Moreover, we show that the problem remains undecidable for PA processes even with respect to the LTL fragment with the only modality until or the fragment with modalities next and infinitely often. 2 L. Bozzelli et al.

The polynomial time decidability of simulation relations for finite state processes: a HORNSAT based approach

1997

Abstract. We present a uniform approach for proving the polynomial time decidability of various simulation and equivalence relations fornite state processes. Our approach involves e cient reductions to the satis ability problem for Horn formulas. It applies directly and naturally to most of the simulation preorders and equivalence relations, studied in the literature. Here we illustrate our methodology by deriving e cient algorithms for a number of such relations.

Verification of Temporal Properties of Concurrent Systems

DAIMI Report Series, 1993

This thesis is concerned with the verification of concurrent systems modelled by process algebras. It provides methods and techniques for reasoning about temporal properties as described by assertions from an expressive modal logic -- the modal µ-calculus. It describes a compositional approach to model checking, efficient local and global algorithms for model checking finite-state systems, a general local fixed-point finding algorithm, a proof system for model checking infinite-state systems, a categorical completeness result for an intuitionistic version of the modal µ-calculus, and finally it shows some novel applications of the logic for expressing behavioural relations.

Model Checking a Logic over Systems with Regular Sets of Processes

2017

Œough systems with process creation give rise to unboundedly many processes, their names are systematically generated and typically form a regular set. When we consider modal logics to specify properties of such systems, it is natural to consider quanti€cation over such regular sets. Œese are in the realm of term modal logics, which are usually undecidable. We consider themonodic variant, in which there is only one free variable in the scope of any modality, and present a model checking algorithm for this logic.

On the complexity of verifying concurrent transition systems

2002

In implementation verification, we check that an implementation is correct with respect to a specification by checking whether the behaviors of a transition system that models the program's implementation correlate with the behaviors of a transition system that models its specification. In this paper, we investigate the effect of concurrency on the complexity of implementation verification. We consider trace-based and tree-based approaches to the verification of concurrent transition systems, with and without fairness.

Formula Based Abstractions of Transition Systems for Real-Time Model Checking

Lecture Notes in Computer Science

When verifying concurrent systems described by transition systems, state explosion is one of the most serious problems. If quantitative temporal information (expressed by clock ticks) are considered, state explosion is even more serious. In this paper we present a non-standard (abstract) semantics for the ASTP language able to produce reduced transition systems. The important point is that the abstract semantics produces transition systems equivalent to the standard ones for what concerns the satisfiability of a given set of formulae of a temporal logic with quantitative modal operators. The equivalence of transition systems with respect to formulae is expressed by means of ρ, n-equivalence: two ρ, n-equivalent transition systems give the same truth value to all formulae such that the actions occurring in the modal operators are contained in ρ, and with time constraints whose values are less than or equal to n.

Formal Verification of Concurrent Systems via Directed Model Checking Abstract

2006

Model checking suffers from the state explosion problem, due to the exponential increase in the size of a finite state model as the number of system components grows. Directed model checking aims at reducing this problem through heuristic-based search strategies. The model of the system is built while checking the formula and this construction is guided by some heuristic function. In this line, we have defined a structure-based heuristic function operating on processes described in the Calculus of Communicating Systems (CCS), which accounts for the structure of the formula to be verified, expressed in the selective Hennessy-Milner logic. We have implemented a tool to evaluate the method and verified a sample of well known CCS processes with respect to some formulae, the results of which are reported and commented.

On the complexity of relational problems for finite state processes

Automata, Languages and …, 1996

We study the complexity of the following two relational problems: Let be a binary relation on nite state processes; and let p0 be a xed nite state process. P1: Determine for processes p and q, if p q. P2: Determine for process p, if p p0. We study the complexities of these problems, when processes are represented by sequential transition systems and by parallel composition of transition systems.

A Uniform Approach for Proving the Polynomial Time Decidability of Simulation Relations for Finite State Processes

1995

We present a uniform approach for proving the polynomial time decidability of various simulation and equivalence relations for finite state processes. Our approach applies directly to a number of simulation relations and equivalences considered in the literature including strong bisimulation [Par81, Mil80, KS90], simulation equivalence [vG90, HT94], readysimulation equivalence [vG90, HT94], complete simulation equivalence [vG90], possibilities equivalence (also known as forward simulation) and backward simulation ...

Formal Verification of Concurrent Systems via Directed Model Checking

Electronic Notes in Theoretical Computer Science, 2007

Model checking suffers from the state explosion problem, due to the exponential increase in the size of a finite state model as the number of system components grows. Directed model checking aims at reducing this problem through heuristic-based search strategies. The model of the system is built while checking the formula and this construction is guided by some heuristic function. In this line, we have defined a structure-based heuristic function operating on processes described in the Calculus of Communicating Systems (CCS), which accounts for the structure of the formula to be verified, expressed in the selective Hennessy-Milner logic. We have implemented a tool to evaluate the method and verified a sample of well known CCS processes with respect to some formulae, the results of which are reported and commented.