17 Automata-theoretic techniques for temporal reasoning (original) (raw)

Effective temporal logics of programs

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.

An automata-theoretic approach to linear temporal logic

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.

The Influence of Temporal Logic on Finite Automata

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.

On the Verification of Temporal Properties

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.

Abstract satisfiability of linear temporal logic

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 ...

Generalized quantitative temporal reasoning: An automata-theoretic approach

Lecture Notes in Computer Science, 1997

This paper proposes an expressive extension to Propositional Linear Temporal Logic dealing with real time correctness properties and gives an automata-theoretic model checking algorithm for the extension. The algorithm has been implemented and applied to examples.