Büchi automaton

About: Büchi automaton is a research topic. Over the lifetime, 1534 publications have been published within this topic receiving 36992 citations. The topic is also known as: Büchi automata.

Automata on infinite objects

Abstract: Publisher Summary This chapter focuses on finite automata on infinite sequences and infinite trees. The chapter discusses the complexity of the complementation process and the equivalence test. Deterministic Muller automata and nondeterministic Buchi automata are equivalent in recognition power. Any nonempty Rabin recognizable set contains a regular tree and shows that the emptiness problem for Rabin tree automata is decidable. The chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree. A short overview of the work that studies the fine structure of the class of Rabin recognizable sets of trees is also presented in the chapter. Depending on the formalism in which tree properties are classified, the results fall in three categories: monadic second-order logic, tree automata, and fixed-point calculi.

Reasoning about Infinite Computations

Abstract: We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping, and repeating) for the automata. It turns out, however that these logics all have the same expressive power and that their decision problems are all PSPACE-complete. We also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem.

An n log n algorithm for minimizing states in a finite automaton

Abstract: An algorithm is given for minimizing the number of states in a finite automaton or for determining if two finite automata are equivalent. The asymptotic running time of the algorithm is bounded by k n log n where k is some constant and n is the number of states. The constant k depends linearly on the size of the input alphabet.

Automata for modeling real-time systems

Abstract: To model the behavior of finite-state asynchronous real-time systems we propose the notion of timed Buchi automata (TBA). TBAs are Buchi automata coupled with a mechanism to express constant bounds on the timing delays between system events. These automata accept languages of timed traces, traces in which each event has an associated real-valued time of occurrence.

Simple on-the-fly automatic verification of linear temporal logic

Abstract: We present a tableau-based algorithm for obtaining an automaton from a temporal logic formula. The algorithm is geared towards being used in model checking in an “on-the-fly” fashion, that is the automaton can be constructed simultaneously with, and guided by, the generation of the model. In particular, it is possible to detect that a property does not hold by only constructing part of the model and of the automaton. The algorithm can also be used to check the validity of a temporal logic assertion. Although the general problem is PSPACE-complete, experiments show that our algorithm performs quite well on the temporal formulas typically encountered in verification. While basing linear-time temporal logic model-checking upon a transformation to automata is not new, the details of how to do this efficiently, and in “on-the-fly” fashion have never been given.