Formal language

About: Formal language is a(n) research topic. Over the lifetime, 5763 publication(s) have been published within this topic receiving 154114 citation(s).

Introduction to Automata Theory, Languages, and Computation

Abstract: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.

A theory of timed automata

Abstract: Alur, R. and D.L. Dill, A theory of timed automata, Theoretical Computer Science 126 (1994) 183-235. We propose timed (j&e) automata to model the behavior of real-time systems over time. Our definition provides a simple, and yet powerful, way to annotate state-transition graphs with timing constraints using finitely many real-valued clocks. A timed automaton accepts timed words-infinite sequences in which a real-valued time of occurrence is associated with each symbol. We study timed automata from the perspective of formal language theory: we consider closure properties, decision problems, and subclasses. We consider both nondeterministic and deterministic transition structures, and both Biichi and Muller acceptance conditions. We show that nondeterministic timed automata are closed under union and intersection, but not under complementation, whereas deterministic timed Muller automata are closed under all Boolean operations. The main construction of the paper is an (PSPACE) algorithm for checking the emptiness of the language of a (nondeterministic) timed automaton. We also prove that the universality problem and the language inclusion problem are solvable only for the deterministic automata: both problems are undecidable (II i-hard) in the nondeterministic case and PSPACE-complete in the deterministic case. Finally, we discuss the application of this theory to automatic verification of real-time requirements of finite-state systems.

Supervisory control of a class of discrete event processes

Abstract: This paper studies the control of a class of discrete event processes, i.e. processes that are discrete, asynchronous and possibly nondeter-ministic. The controlled process is described as the generator of a formal language, while the controller, or supervisor, is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior. The existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language. Two examples are provided.

The empirical case for two systems of reasoning.

Abstract: Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations reflect similarity structure and relations of temporal contiguity. The other is "rule based" because it operates on symbolic structures that have logical content and variables and because its computations have the properties that are normally assigned to rules. The systems serve complementary functions and can simultaneously generate different solutions to a reasoning problem. The rule-based system can suppress the associative system but not completely inhibit it. The article reviews evidence in favor of the distinction and its characterization. One of the oldest conundrums in psychology is whether people are best conceived as parallel processors of information who operate along diffuse associative links or as analysts who operate by deliberate and sequential manipulation of internal representations. Are inferences drawn through a network of learned associative pathways or through application of a kind of"psychologic" that manipulates symbolic tokens in a rule-governed way? The debate has raged (again) in cognitive psychology for almost a decade now. It has pitted those who prefer models of mental phenomena to be built out of networks of associative devices that pass activation around in parallel and distributed form (the way brains probably function) against those who prefer models built out of formal languages in which symbols are composed into sentences that are processed sequentially (the way computers function). An obvious solution to the conundrum is to conceive of the

An axiomatic basis for computer programming

Abstract: In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference which can be used in proofs of the properties of computer programs. Examples are given of such axioms and rules, and a formal proof of a simple theorem is displayed. Finally, it is argued that important advantages, both theoretical and practical, may follow from a pursuance of these topics.