17 Automata-theoretic techniques for temporal reasoning

Time and Logic, 2019

In this chapter we investigate effective proof systems for temporal logics both propositional and first-order. The issue of effective proof systems for propositional temporal logic is much easier than for the first-order one. Partly because of this and partly because of applications we dwell on the first-order case much longer than on the propositional case. We prove soundness and completeness theorems for various effective proof systems and compare the program verifying-power of those systems.

Logics for concurrency, 1996

The automata-theoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over some alphabet. Thus, programs and specifications can be viewed as descriptions of languages over some alphabet. The automata-theoretic perspective considers the relationships between programs and their specifications as relationships between languages. By translating programs and specifications to automata, questions about programs and their specifications can be reduced to questions about automata. More specifically, questions such as satisfiability of specifications and correctness of programs with respect to their specifications can be reduced to questions such as nonemptiness and containment of automata. Unlike classical automata theory, which focused on automata on finite words, the applications to program specification, verification, and synthesis, use automata on infinite words, since the computations in which we are interested are typically infinite. This paper provides an introduction to the theory of automata on infinite words and demonstrates its applications to program specification, verification, and synthesis.

Al-Rafidain Engineering Journal (AREJ)

The theory of automata combines ideas from engineering, linguistics, mathematics, philosophy, etc. The Entscheidungsproblem asks if it is possible to design a series of steps that replaces a mathematician. An automaton is an abstract machine that processes data. C. Shannon's theory is today's most popular despite having no relationship with the other. The Kt system is called "minimal" because it makes no assumptions about the structure of time. In LKt, we have four monary temporal operators, F, P, G and H, which are mutually interdefinable. Interdefinability means that we will pass logic in the future is the same as saying I will never fail logic, interpreting not passing logic as failing logic. The minimal system syntax of temporal logic introduces operators that have the property of being defined in terms of others. Modal logic studies the reasoning that involves the use of expressions "necessarily" and "possibly". In this article, we will represent through a finite automaton the temporal logic formula Fp. It allows us to see an acceptance pattern for Fp by considering two variables: p and q. Kt's axiomatic system of time expresses the idea that both the present and the past are fixed, if it has always been in the past that it will be some time in the future that p is now. No philosophical argument supports deterministic time flow; the logic of time must be open.Temporal logic has revived many old problems, from the Megaric-Stoics to the minimal system of temporal logic. Our work suggests that the future operators of system Kt follow an evaluation pattern, but we must be cautious because this pattern can only apply to models whose time flow is based on instants and precedence relations.

Theoretical Computer Science, 1995

... Theoretical Computer Science ELSEVIER Theoretical Computer Science 140 (1995) 95138 On using temporal logic for refinement and compositional verification of concurrent systems Abdelillah Mokkedem*, Dominique Mery CRINCNRS INRIALorraine, BP239, 54506 ...

Protocol Specification, Testing and Verification, Xiii: Proceedings of the IFIP TC6/WG6. 1. Thirteenth International Symposium on Protocol Specification, Testing and Verification, Liége, Belgium, 25-28 May, 1993, 1993

We present a new algorithm that can be used for solving the model−checking problem for linear−time temporal logic. This algorithm can be viewed as the combination of two existing algorithms plus a new state representation technique introduced in this paper. The new algorithm is simpler than the traditional algorithm of Tarjan to check for maximal strongly connected components in a directed graph which is the classical algorithm used for model−checking. It has the same time complexity as Tarjan's algorithm, but requires less memory. Our algorithm is also compatible with other important complexity management techniques, such as bit−state hashing and state space caching.

2007

Increasing interest towards property based design calls for effective satisfiability procedures for expressive temporal logics, e.g. the IEEE standard Property Specification Language (PSL). In this paper, we propose a new approach to the satisfiability of PSL formulae; we follow recent approaches to decision procedures for Satisfiability Modulo Theory, typically applied to fragments of First Order Logic. The underlying intuition is to combine two interacting search mechanisms: on one side, we search for assignments that satisfy the Boolean abstraction of the problem; on the other, we invoke a solver for temporal satisfiability on the conjunction of temporal formulae corresponding to the assignment. Within this framework, we explore two directions. First, given the fixed polarity of each constraint in the theory solver, aggressive simplifications can be applied. Second, we analyze the idea of conflict reconstruction: whenever a satisfying assignment at the level of the Boolean abstraction results in a temporally unsatisfiable problem, we identify inconsistent subsets that can be used to rule out possibly many other assignments. We propose two methods to extract conflict sets on conjunctions of temporal formulae (one based on BDD-based Model Checking, and one based on SAT-based Simple Bounded Model Checking). We analyze the limits and the merits of the approach with a thorough experimental evaluation. a counterexample trace: the user is working at the level of requirements, and thus the inconsistency should be identified at the same level, e.g. as a subset of inconsistent requirements. Furthermore, this approach may have some limitations: in fact, techniques and tools for temporal logic model checking are focusing on complexity in the model, and even reductions on the temporal logic formula [ST03] are oriented to dominating the complexity in the model.

2001

Abstract. Model Checking has become one of the most powerful methods for automatic verification of software systems. But this technique is only directly applicable to small or medium size systems. For large systems, it suffers from the state explosion problem. One of the most promising ways to solve this problem is the use of Abstract Interpretation to construct simpler models of the system, where the interesting properties can be analyzed. In this paper, we present a theoretical language-independent framework to assist in the ...

Refinement Techniques in Software Engineering, 2006

Electronic Proceedings in Theoretical Computer Science, 2017

In this paper, we address the problem of model checking temporal properties of finite-state programs.