17 Automata-theoretic techniques for temporal reasoning

State machines are considered a very general means of expressing computations in an implementation-independent way. There are also ways to extend the general state machine framework with distribution aspects. However, there is still no complete agreement when it comes to handling time in this framework. In this article we take a look at existing ways to enhance state machine frameworks. Based on this, we propose a general framework of time extensions for state machines, which we relate to existing approaches. Our mainly addresses time approaches for ASM, because ASM are considered a very general state machine model. Taking this into account, our approach is valid for state-transition systems in general.

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.

Computing Meaning, 2008

Finite-state descriptions for temporal semantics are outlined through which to distinguish soft inferences reflecting manners of conceptualization from more robust semantic entailments defined over models. Just what descriptions are built (before being interpreted model-theoretically) and how they are grounded in models of reality explain (upon examination) why some inferences are soft.

2012

Finite State Automata Semantics in Communicating Sequential Processes: Traditionally, distributed systems and protocols are described with finite state automata. Later on, other more powerful mathematical tools for specification and analyses of distributed systems have been developed, such as Petri nets, CSP etc. Modern tools and notations for specification, development and implementation of distributed systems are based on them. In commercial tools, that use finite state automata, as a base for business process specification, the problem is the need to convert older specifications into new one without losing the semantics. Newly developed tools are based on Petri nets or CSP. They are more powerful in specification and analyses, but they have to support continuity. Intention of this paper is formally to specify finite state automata in CSP. Finite state automata semantics is clear, but there are needs for conversion of business processes specified in them to new form without losing the semantics.

Lecture Notes in Computer Science, 2010

Amir has had a profound influence on the three of us, as a teacher, an advisor, a mentor, and a collaborator. His fundamental ideas on the temporal logics of programs have, to a large extent, set the course for our professional careers. His sudden passing away has deprived us of many more years of wonderful interaction, intellectual engagement, and friendship. We miss him profoundly. His wisdom and pleasantness will stay with us forever.

1999

Abstract A specification formalism for reactive systems defines a class of!-languages. We call a specification formalism fully decidable if it is constructively closed under boolean operations and has a decidable satisfiability nonemptiness problem. There are two important, robust classes of!-languages that are definable by fully decidable formalisms. The!-regular languages are definable by finite automata, or equivalently, by the Sequential Calculus.

2003

We introduce a logic for sequential, non distributed Abstract State Machines. Unlike other logics for ASMs which are based on dynamic logic, our logic is based on atomic propositions for the function updates of transition rules. We do not assume that the transition rules of ASMs are in normal form, for example, that they concern distinct cases. Instead we allow structuring concepts of ASM rules including sequential composition and possibly recursive submachine calls. We show that several axioms that have been proposed for reasoning about ASMs are derivable in our system and that the logic is complete for hierarchical (non-recursive) ASMs.

The aim of this paper is to introduce a certain kind of information state representation in a dynamic system of propositional logic, using finite state automatons and highlight its advantages, including relation to inquisitive semantics and belief revision.

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.