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37 produkter
37 produkter
Inbunden, Engelska, 1997
1 524 kr
Skickas inom 10-15 vardagar
In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.
Del 21 - Progress in Computer Science and Applied Logic
Automata Theory and its Applications
Inbunden, Engelska, 2001
549 kr
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The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.
Inbunden, Engelska, 1985
1 772 kr
Skickas inom 11-20 vardagar
E-bok
PDF, Engelska, 2012712 kr
Läs direkt efter köp
The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin''s 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist''s toolbox. Suppose that we take a computer scientist''s point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi''s SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin''s S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.
E-bok
PDF, Engelska, 2012687 kr
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In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.
Del 21 - Progress in Computer Science and Applied Logic
Automata Theory and its Applications
Häftad, Engelska, 2012
549 kr
Skickas inom 10-15 vardagar
The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.
Häftad, Engelska, 2012
549 kr
Skickas inom 10-15 vardagar
In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.
E-bok
PDF, Engelska, 20121 174 kr
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In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the recent dramatic growth in the applications of logic to computer science. Thus our choice of topics has been heavily influenced by such applications. Of course, we cover the basic traditional topics - syntax, semantics, soundness, completeness and compactness - as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much of our book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic, especially in its application to Logic Programming and PROLOG. We deal extensively with the mathematical foundations of all three of these subjects. In addition, we include two chapters on nonclassical logic- modal and intuitionistic - that are becoming increasingly important in computer science. We develop the basic material on the syntax and se mantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method introduced for classical logic. We indicate how it can easily be adapted to various other special types of modal log ics. A number of more advanced topics (including nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.
Häftad, Engelska, 2019
549 kr
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This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2020, held in Deerfield Beach, FL, USA, in January 2020. The 17 revised full papers were carefully reviewed and selected from 30 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.
E-bok
PDF, Engelska, 2019712 kr
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This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2020, held in Deerfield Beach, FL, USA, in January 2020. The 17 revised full papers were carefully reviewed and selected from 30 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.
Del 13137 - Lecture Notes in Computer Science
Logical Foundations of Computer Science
International Symposium, LFCS 2022, Deerfield Beach, FL, USA, January 10–13, 2022, Proceedings
Häftad, Engelska, 2021
820 kr
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This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2022, held in Deerfield Beach, FL, USA, in January 2022.The 23 revised full papers were carefully reviewed and selected from 35 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.
E-bok
Engelska, 2021993 kr
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This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2022, held in Deerfield Beach, FL, USA, in January 2022. The 23 revised full papers were carefully reviewed and selected from 35 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.
Häftad, Engelska, 2023
657 kr
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The theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or “donut”) is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric “chord-and-tangent” method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.
764 kr
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The theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or “donut”) is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric “chord-and-tangent” method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.
631 kr
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Del 9537 - Lecture Notes in Computer Science
Logical Foundations of Computer Science
International Symposium, LFCS 2016, Deerfield Beach, FL, USA, January 4-7, 2016. Proceedings
Häftad, Engelska, 2015
565 kr
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This bookconstitutes the refereed proceedings of the International Symposium on LogicalFoundations of Computer Science, LFCS 2016, held in Deerfield Beach, FL, USA inJanuary 2016. The 27 revised full paperswere carefully reviewed and selected from 46 submissions. The scopeof the Symposium is broad and includes constructive mathematics and typetheory; homotopy type theory; logic, automata, and automatic structures;computability and randomness; logical foundations of programming; logicalaspects of computational complexity; parameterized complexity; logicprogramming and constraints; automated deduction and interactive theoremproving; logical methods in protocol and program verification; logical methodsin program specification and extraction; domain theory logics; logicalfoundations of database theory; equational logic and term rewriting; lambda andcombinatory calculi; categorical logic and topological semantics; linear logic;epistemic and temporal logics; intelligent and multiple-agent system logics;logics of proof and justification; non-monotonic reasoning; logic in gametheory and social software; logic of hybrid systems; distributed system logics;mathematical fuzzy logic; system design logics; and other logics in computerscience.
E-bok
PDF, Engelska, 2015714 kr
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This bookconstitutes the refereed proceedings of the International Symposium on LogicalFoundations of Computer Science, LFCS 2016, held in Deerfield Beach, FL, USA inJanuary 2016. The 27 revised full paperswere carefully reviewed and selected from 46 submissions. The scopeof the Symposium is broad and includes constructive mathematics and typetheory; homotopy type theory; logic, automata, and automatic structures;computability and randomness; logical foundations of programming; logicalaspects of computational complexity; parameterized complexity; logicprogramming and constraints; automated deduction and interactive theoremproving; logical methods in protocol and program verification; logical methodsin program specification and extraction; domain theory logics; logicalfoundations of database theory; equational logic and term rewriting; lambda andcombinatory calculi; categorical logic and topological semantics; linear logic;epistemic and temporal logics; intelligent and multiple-agent system logics;logics of proof and justification; non-monotonic reasoning; logic in gametheory and social software; logic of hybrid systems; distributed system logics;mathematical fuzzy logic; system design logics; and other logics in computerscience.
Del 10703 - Lecture Notes in Computer Science
Logical Foundations of Computer Science
International Symposium, LFCS 2018, Deerfield Beach, FL, USA, January 8–11, 2018, Proceedings
Häftad, Engelska, 2017
565 kr
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This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2018, held in Deerfield Beach, FL, USA, in January 2018.The 22 revised full papers were carefully reviewed and selected from 22 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda andcombinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; and other logics in computer science.
E-bok
Engelska, 2017708 kr
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This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2018, held in Deerfield Beach, FL, USA, in January 2018.The 22 revised full papers were carefully reviewed and selected from 22 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda andcombinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; and other logics in computer science.
E-bok
PDF, Engelska, 2006364 kr
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The courses given at the 1st C.I.M.E. Summer School of 1988 dealt with the main areas on the borderline between applied logic and theoretical computer science. These courses are recorded here in five expository papers: S. Homer: The Isomorphism Conjecture and its Generalization.- A. Nerode: Some Lectures on Intuitionistic Logic.- R.A. Platek: Making Computers Safe for the World. An Introduction to Proofs of Programs. Part I. - G.E. Sacks: Prolog Programming.- A. Scedrov: A Guide to Polymorphic Types.
E-bok
PDF, Engelska, 2003712 kr
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Del 1429 - Lecture Notes in Mathematics
Logic and Computer Science
Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Montecatini Terme, Italy, June 20-28, 1988
Häftad, Engelska, 1990
278 kr
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The courses given at the 1st C.I.M.E. Summer School of 1988 dealt with the main areas on the borderline between applied logic and theoretical computer science. These courses are recorded here in five expository papers: S. Homer: The Isomorphism Conjecture and its Generalization.- A. Nerode: Some Lectures on Intuitionistic Logic.- R.A. Platek: Making Computers Safe for the World. An Introduction to Proofs of Programs. Part I. - G.E. Sacks: Prolog Programming.- A. Scedrov: A Guide to Polymorphic Types.
Häftad, Engelska, 1992
549 kr
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This volume presents the papers selected for the SymposiumLogic at Tver '92, held at Sokol, near Tver, Russia in July1992. It is the second in a series of international symposiaon logical foundations of computer science held in Russia.The meeting is a joint effort of scholars from both theformer Soviet Union and the West, and indicates a new era ofinternational cooperation. Sponsors of the meeting include:the Association for Computing Machinery, the Association forSymbolic Logic, andthe Committee on MathematicalFoundations of Computer Science of IEEE.The book is a unique source of information on the state ofcomputer science research in the former Soviet Union andpresents important discoveries in the area of logicalfoundations of computer science.
Häftad, Engelska, 1993
550 kr
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Hybrid systems are networks of interacting digital andanalog devices. Control systems for inherently unstableaircraft and computer aided manufacturing are typicalapplications for hybrid systems, but due to the rapiddevelopment of processor and circuit technology modern carsand consumer electronics use software to control physicalprocesses. The identifying characteristic of hybrid systemsis that they incorporate both continuous components governedby differential equations and also digital components -digital computers, sensors, and actuators controlled byprograms.This volume of invited refereed papers is inspired by aworkshop on the Theory of Hybrid Systems, held at theTechnical University, Lyngby, Denmark, in October 1992, andby a prior Hybrid Systems Workshop, held at CornellUniversity, USA, in June 1991, organized by R.L. Grossmanand A. Nerode. Some papers are the final versions of paperspresented at these workshops and some are invited papersfrom other researchers who were not able to attend theseworkshops.
Häftad, Engelska, 1994
550 kr
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This volume presents the refereed papers accepted for the international symposium Logical Foundations of Computer Science '94, Logic at St. Petersburg, held in St. Petersburg, Russia in July 1994. The symposium was the third in a series of joint efforts of logicians from both the former Soviet Union and the West.The volume reflects that the interaction of logic and computer science is an especially fertile ground for interdisciplinary work providing mutual understanding and benefits. The totally 35 papers are devoted to topics as linear logic, Horn clauses, model-checking, lambda-calculi, modal logic, and problem complexity.
Häftad, Engelska, 1995
566 kr
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This volume contains the revised refereed papers accepted for presentation at the Third International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR '95, held in Lexington, KY, USA in June 1995 under the sponsorship of the Association for Logic Programming.The LPNMR conferences bring together researchers from logic programming and the logical foundations of artificial intelligence in order to facilitate cooperation and cross-fertilization of ideas. The 28 full papers presented define the state of the art in this interdisciplinary area of research, which has recently attracted much interest.
Häftad, Engelska, 1995
550 kr
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This book documents the scientific outcome of the Third International Workshop on Hybrid Systems, held in Ithaca, NY, USA, in October 1994. It presents a selection of carefully reviewed and revised full papers chosen from the workshop contribution and is the successor to LNCS 736, the seminal "Hybrid Systems" volume edited by Grossman, Nerode, Ravn, and Rischel.Hybrid systems are models for networks of digital and continuous devices, in which digital control programs sense and supervise continuous and discrete plants governed by differential or difference equations. The investigation of hybrid systems is creating a new and fascinating discipline bridging mathematics, computer science, and control engineering.
Häftad, Engelska, 1997
550 kr
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This book constitutes the refereed proceedings of the 4th International Symposium on Logical Foundations of Computer Science, LFCS'97, held in Yaroslavl, Russia, in July 1997.The volume presents 42 revised refereed papers carefully selected by the program committee. All current issues of computer science logic are addressed. There is a certain emphasis on reporting the progress achieved by scientists from various parts of the former Soviet Union; but there are also many other strong papers from the international research community.
Häftad, Engelska, 1997
566 kr
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This book constitutes the refereed proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR '97, held in Dagstuhl Castle, Germany, in July 1997.The volume presents 19 revised regular papers together with 10 system descriptions and five abstracts of invited presentations. The papers included report state-of-the-art research and development in the interdisciplinary area of logic programming and logical foundations of artificial intelligence.
Häftad, Engelska, 1997
566 kr
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This book constitutes the thoroughly refereed post-conference documentation of the Fourth International Conference on Hybrid Systems held in Ithaca, NY, USA, in October 1996. The volume presents 19 carefully revised full papers selected from numerous submissions. Hybrid systems research focuses on modeling, design, and validation of interacting systems (plants) and computer programs (control automata). This volume is devoted to hybrid systems models, formal verification, computer simulation, goal reachability, algorithms for extracting hybrid control programs, and application models for avionics, highway traffic control, and air traffic control.