Formal language

About: Formal language is a research topic. Over the lifetime, 5763 publications have been published within this topic receiving 154114 citations.

A Computational Account for a Description Logic of Time and Action

Abstract: A formal language for representing and reasoning about time and action is presented. We employ an action representation in the style of Allen, where an action is represented by describing the time course of events while the action occurs. In this sense, an action is defined by means of temporal constraints on the world states, which pertain to the action itself, and on other more elementary actions occurring over time. A distinction between action types and individual actions is supported by the formalism. Plans are seen as complex actions whose properties possibly change with time. The formal representation language used in this paper is a description logic, and it is provided with a well founded syntax, semantics and calculus. Algorithms for the subsumption and recognition tasks - forming the basis for action management - are provided.

Automata, computability and complexity : theory and applications

Abstract: PART I: INTRODUCTION 1 Why Study Automata Theory? 2 Review of Mathematical Concepts 2.1 Logic 2.2 Sets 2.3 Relations 2.4 Functions 2.5 Closures 2.6 Proof Techniques 2.7 Reasoning about Programs 2.8 References 3 Languages and Strings 3.1 Strings 3.2 Languages 4 The Big Picture: A Language Hierarchy 4.1 Defining the Task: Language Recognition 4.2 The Power of Encoding 4.3 A Hierarchy of Language Classes 5 Computation 5.1 Decision Procedures 5.2 Determinism and Nondeterminism 5.3 Functions on Languages and Programs PART II: FINITE STATE MACHINES AND REGULAR LANGUAGES 6 Finite State Machines 6.2 Deterministic Finite State Machines 6.3 The Regular Languages 6.4 Programming Deterministic Finite State Machines 6.5 Nondeterministic FSMs 6.6 Interpreters for FSMs 6.7 Minimizing FSMs 6.8 Finite State Transducers 6.9 Bidirectional Transducers 6.10 Stochastic Finite Automata 6.11 Finite Automata, Infinite Strings: Buchi Automata 6.12 Exercises 7 Regular Expressions 7.1 What is a Regular Expression? 7.2 Kleene's Theorem 7.3 Applications of Regular Expressions 7.4 Manipulating and Simplifying Regular Expressions 8 Regular Grammars 8.1 Definition of a Regular Grammar 8.2 Regular Grammars and Regular Languages 8.3 Exercises 9 Regular and Nonregular Languages 9.1 How Many Regular Languages Are There? 9.2 Showing That a Language Is Regular.124 9.3 Some Important Closure Properties of Regular Languages 9.4 Showing That a Language is Not Regular 9.5 Exploiting Problem-Specific Knowledge 9.6 Functions on Regular Languages 9.7 Exercises 10 Algorithms and Decision Procedures for Regular Languages 10.1 Fundamental Decision Procedures 10.2 Summary of Algorithms and Decision Procedures for Regular Languages 10.3 Exercises 11 Summary and References PART III: CONTEXT-FREE LANGUAGES AND PUSHDOWN AUTOMATA 144 12 Context-Free Grammars 12.1 Introduction to Grammars 12.2 Context-Free Grammars and Languages 12.3 Designing Context-Free Grammars 12.4 Simplifying Context-Free Grammars 12.5 Proving That a Grammar is Correct 12.6 Derivations and Parse Trees 12.7 Ambiguity 12.8 Normal Forms 12.9 Stochastic Context-Free Grammars 12.10 Exercises 13 Pushdown Automata 13.1 Definition of a (Nondeterministic) PDA 13.2 Deterministic and Nondeterministic PDAs 13.3 Equivalence of Context-Free Grammars and PDAs 13.4 Nondeterminism and Halting 13.5 Alternative Definitions of a PDA 13.6 Exercises 14 Context-Free and Noncontext-Free Languages 14.1 Where Do the Context-Free Languages Fit in the Big Picture? 14.2 Showing That a Language is Context-Free 14.3 The Pumping Theorem for Context-Free Languages 14.4 Some Important Closure Properties of Context-Free Languages 14.5 Deterministic Context-Free Languages 14.6 Other Techniques for Proving That a Language is Not Context-Free 14.7 Exercises 15 Algorithms and Decision Procedures for Context-Free Languages 15.1 Fundamental Decision Procedures 15.2 Summary of Algorithms and Decision Procedures for Context-Free Languages 16 Context-Free Parsing 16.1 Lexical Analysis 16.2 Top-Down Parsing 16.3 Bottom-Up Parsing 16.4 Parsing Natural Languages 16.5 Stochastic Parsing 16.6 Exercises 17 Summary and References PART IV: TURING MACHINES AND UNDECIDABILITY 18 Turing Machines 18.1 Definition, Notation and Examples 18.2 Computing With Turing Machines 18.3 Turing Machines: Extensions and Alternative Definitions 18.4 Encoding Turing Machines as Strings 18.5 The Universal Turing Machine 18.6 Exercises 19 The Church-Turing 19.1 The Thesis 19.2 Examples of Equivalent Formalisms 20 The Unsolvability of the Halting Problem 20.1 The Language H is Semidecidable but Not Decidable 20.2 Some Implications of the Undecidability of H 20.3 Back to Turing, Church, and the Entscheidungsproblem 21 Decidable and Semidecidable Languages 21.2 Subset Relationships between D and SD 21.3 The Classes D and SD Under Complement 21.4 Enumerating a Language 21.5 Summary 21.6 Exercises 22 Decidability and Undecidability Proofs 22.1 Reduction 22.2 Using Reduction to Show that a Language is Not Decidable 22.3 Rice's Theorem 22.4 Undecidable Questions About Real Programs 22.5 Showing That a Language is Not Semidecidable 22.6 Summary of D, SD/D and (R)SD Languages that Include Turing Machine Descriptions 22.7 Exercises 23 Undecidable Languages That Do Not Ask Questions about Turing Machines 23.1 Hilbert's 10th Problem 23.2 Post Correspondence Problem 23.3 Tiling Problems 23.4 Logical Theories 23.5 Undecidable Problems about Context-Free Languages APPENDIX C: HISTORY, PUZZLES, AND POEMS 43 Part I: Introduction 43.1 The 15-Puzzle Part II: Finite State Machines and Regular Languages 44.1 Finite State Machines Predate Computers 44.2 The Pumping Theorem Inspires Poets REFERENCES INDEX Appendices for Automata, Computability and Complexity: Theory and Applications: * Math Background* Working with Logical Formulas* Finite State Machines and Regular Languages* Context-Free Languages and PDAs* Turing Machines and Undecidability* Complexity* Programming Languages and Compilers* Tools for Programming, Databases and Software Engineering* Networks* Security* Computational Biology* Natural Language Processing* Artificial Intelligence and Computational Reasoning* Art & Entertainment: Music & Games* Using Regular Expressions* Using Finite State Machines and Transducers* Using Grammars

Introducing the ITP Tool: a Tutorial

Abstract: We present a tutorial of the ITP tool, a rewriting-based theorem prover that can be used to prove inductive properties of membership equational specifications. We also introduce membership equational logic as a formal language particularly ad- equate for specifying and verifying semantic data structures, such as ordered lists, binary search trees, priority queues, and powerlists. The ITP tool is a Maude program that makes extensive use of the reflective capabilities of this system. In fact, rewriting- based proof simplification steps are directly executed by the powerful underlying Maude rewriting engine. The ITP tool is currently available as a web-based application that includes a module editor, a formula editor, and a command editor. These editors allow users to create and modify their specifications, to formalize properties about them, and to guide their proofs by filling and submitting web forms.

Formal Specification of User Interfaces: A Comparison and Evaluation of Four Axiomatic Approaches

Abstract: Few examples of formal specification of the semantics of user interfaces exist in the literature. This paper presents a comparison of four axiomatic approaches which we have applied to the specification of a commercial user interface–the line editor for the Tandy PC-1 Pocket Computer. These techniques are shown to result in complete and relatively concise descriptions. A number of useful and nontrivial properties of the interface are formally deduced from one of the specifications. In addition, a direct implementation of the interface is constructed from a formal specification. Limitations of these specification examples are discussed along with future research work.

Regular Cost Functions over Finite Trees

Abstract: We develop the theory of regular cost functions over finite trees: aquantitative extension to the notion of regular languages of trees: Cost functions map each input (tree) to a value in~$\omega+1$, and are considered modulo an equivalence relation which forgets about specific values, but preserves boundedness of functions on all subsets of the domain. We introduce nondeterministic and alternating finite tree cost automata for describing cost functions. We show that all these forms of automata are effectively equivalent. We also provide decision procedures for them. Finally, following B\"uchi's seminal idea, we use cost automata for providing decision procedures for cost monadic logic, a quantitative extension of monadic second order logic.