Find out how to access previewonly content
Date:
30 Jul 2005
Theory of computation over stream algebras, and its applications
 J. V. Tucker,
 J. I. Zucker
 … show all 2 hide
Abstract
The theory of computable functions on abstract data types is outlined. Methods for extending the theory to establish the scope and limits of computation on streams over abstract data types arc described. Applications of these methods to the theory of synchronous concurrent algorithms are discussed.
 J A Bergstra and J V Tucker, A characterisation of computable data types by means of a finite equational specification method, in J W de Bakker and J van Leeuwen (eds.) Automata, Languages and Programming, Seventh Colloquium, Noordwijkerhout, 1980, Springer Lecture Notes in Computer Science 81, SpringerVerlag, Berlin, 1980, pp. 76–90.
 J A Bergstra and J V Tucker, Algebraic specifications of computable and semicomputable data types, Theoretical Computer Science, 50 (1987) 137–181. CrossRef
 J A Bergstra and J V Tucker, Initial and final algebra semantics for data type specifications: two characterisation theorems, Society for Industrial and Applied Mathematics (SIAM) J on Computing, 12 (1983) 366–387.
 L Blum, M Shub and S Smale, On a theory of computation and complexity over the real numbers: NPcompleteness, recursive functions and universal machines, Bulletin American Mathematical Society 21 (1989) 1–46. CrossRef
 B Courcelle, Recursive applicative program schemes, in J van Leeuwen (ed) Handbook of Theoretical Computer Science. Volume B: Formal Models and Semantics, Elsevier, 1990, 459–492.
 J P Crutchfield and K Kaneko, Phenomenology of spatiotemporal chaos, in H Bailin (ed.) Directions in Chaos, World Scientific, 1987.
 H Ehrig and B Mahr, Fundamentals of Algebraic Specifications 1 — Equations and initial semantics, SpringerVerlag, 1985.
 S M Eker, V Stavridou and J V Tucker, Verification of synchronous concurrent algorithms using OBJ3. A case study of the Pixel Planes architecture, In G Jones and M Sheeran (eds.) Designing Correct Circuits, SpringerVerlag, 1991, pp. 231–252.
 S M Eker and J V Tucker, Specification, derivation and verification of concurrent line drawing algorithms and architectures, in R A Earnshaw (ed.), Theoretical Foundations of Computer Graphics and CAD, SpringerVerlag, 1988, pp. 449–516.
 S M Eker and J V Tucker, Specification and verification of synchronous concurrent algorithms: a case study of the Pixel Planes architecture, in P M Dew, R A Earnshaw and T R Heywood (eds.), Parallel Processing for Computer Vision and Display, Addison Wesley, 1989, pp.16–49.
 J E Fenstad, General Recursion Theory: An Axiomatic Approach, SpringerVerlag, Berlin, 1980.
 M Fitting, Fundamentals of Generalised Recursion Theory, NorthHolland, Amsterdam, 1981.
 F Fogelman Soulie, Y Robert, M Tchuente (eds.), Automata Networks in Computer Science, Manchester University Press, 1986.
 J A Goguen, J W Thatcher, E G Wagner, and J B Wright, An initial algebra approach to the specification, correctness and implementation of abstract data types, in R T Yeh (ed.), Current Trends in Programming Methodology: IV Data Structuring, Prentice Hall, 1978, pp. 80–149.
 S Greibach, Theory of Program Structures: Schemes, Semantics, Verification, Springer Lecture Notes in Computer Science 36, Berlin, 1975.
 N A Harman and J V Tucker, Clocks, retimings, and the formal specification of a UART, in G Milne (ed.) The Fusion of Hardware Design and Verification (Proceedings of IFIP Working Group 10.2 Working Conference), NorthHolland, 1988, pp. 375–396.
 N A Harman and J V Tucker, The formal specification of a digital correlator I: User specification process, in K McEvoy and J V Tucker [90], pp. 161–262.
 L A Harrington et al. (eds.) Harvey Friedman's Research on the Foundations of Mathematics, NorthHolland, 1985.
 K M Hobley, B C Thompson, and J V Tucker, Specification and verification of synchronous concurrent algorithms: a case study of a convolution algorithm, in G Milne (ed.) The Fusion of Hardware Design and Verification (Proceedings of IFIP Working Group 10.2 Working Conference), NorthHolland, 1988, pp. 347–374.
 A V Holden, J V Tucker and B C Thompson, The computational structure of neural systems, in A V Holden and V I Kryukov (eds.) Neurocomputers and Attention. I: Neurobiology, Synchronisation and Chaos, Manchester University Press, 1990, 223–240.
 A V Holden, J V Tucker and B C Thompson, Can excitable media be considered as computational systems? Physica D 49 (1991) 240–246. CrossRef
 A V Holden, J V Tucker and H Zhang, Coupled map lattices as computational systems, Computer Science Division Research Report, University College of Swansea, 1992.
 G Kahn, The semantics of a simple language for parallel processing, in Proceedings IFIP Congress 74, IFIP, 1974, 471–475
 K Kaneko (ed.), Coupled Map Lattices — Theory and Applications, J Wiley, in press.
 D Kozen and J Tiuryn, Logics of programs, in J van Leeuwen (ed) Handbook of Theoretical Computer Science. Volume B: Formal Models and Semantics, Elsevier, 1990, 789–840.
 A R Martin and J V Tucker, The concurrent assignment representation of synchronous systems, Parallel Computing 9 (1988/89) 227–256. CrossRef
 K McEvoy and J V Tucker (eds.), Theoretical Foundations of VLSI Design, Cambridge University Press, 1990.
 B McConnell and J V Tucker, Infinite synchronous concurrent algorithms: the specifiation and verification of a hardware stack, in H Schwichtenberg (ed.) Logic and Algebra for Specification, SpringerVerlag, 1992.
 K Meinke, Universal algrebra in higher types, Theoretical Computer Science, to appear.
 K Meinke and J V Tucker, Specification and representation of synchronous concurrent algorithms, in F H Vogt (ed.) Concurrency '88, Springer Lecture Notes in Computer Science 335, SpringerVerlag, 1988, pp. 163–180.
 K Meinke and J V Tucker, Universal algebra, in S Abramsky, D Gabbay, T S E Maibaum (eds.) Handbook of Logic in Computer Science, Oxford University Press, pp. 189–411.
 J C Shepherdson, Algorithmic procedures, generalised Turing algorithms, and elementary recursion theory, in Harrington et al. [1985], pp. 285–308.
 R Stephens and B C Thompson, Composition of cartesian stream transformers, in preparation.
 B C Thompson, A mathematical theory of synchronous concurrent algorithms. PhD Thesis, School of Computer Studies, University of Leeds, 1987.
 B C Thompson and J V Tucker, Theoretical considerations in algorithm design, in R A Earnshaw (ed.), Fundamental Algorithms for Computer Graphics, SpringerVerlag, 1985, pp. 855–878.
 B C Thompson and J V Tucker, Algebraic specification of synchronous concurrent algorithms and architectures, Computer Science Division Research Report, University College of Swansea, 1991.
 J V Tucker, Computing in algebraic systems, in F.R. Drake and S.S. Wainer (eds.) Recursion Theory, its Generalisations and Applications, London Mathematical Society Lecture Note Series 45, Cambridge University Press, Cambridge, 1980, pp. 215–235.
 J V Tucker, Theory of computation and specification over abstract data types and its applications, in F L Bauer (ed), Proceedings of NATO Summer School 1989 at Marktoberdorf, in Logic, algebra and computation, Springer, 1991, pp 1–39.
 J V Tucker and J I Zucker, Program Correctness over Abstract Data Types, with Error State Semantics, North Holland, 1988.
 J V Tucker and J I Zucker, Horn programs and semicomputable relations on abstract structures, Automata, Languages and Programming 1989, Proceedings of the Sixteenth Colloquium, Stresa, Springer Lecture Notes in Computer Science 372, SpringerVerlag, 1989, pp.745–760
 J V Tucker, S S Wainer and J I Zucker, Provably computable functions on abstract data types, Automata, Languages and Programming 1990, Proceedings of the Seventeenth Colloquium, Coventry, Springer Lecture Notes in Computer Science, SpringerVerlag, 1990.
 J V Tucker and J I Zucker, Projections of semicomputable relations on abstract data types, International J of Foundations of Computer Science 2 (1991) 267–296. CrossRef
 J V Tucker and J I Zucker, Deterministic and nondeterministic computation, and Horn programs, on abstract data types, Journal of Logic Programming, 13 (1992) 23–55. a. CrossRef
 J V Tucker and J I Zucker, Examples of semicomputable sets of real and complex numbers, in J P Myers and M J O'Donnell (eds.), Constructivity in Computer Science, Springer Lecture Notes in Computer Science, Berlin. b.
 J V Tucker and J I Zucker, Provable computable selection functions on abstract structures, in P Aczel, H Simmons and S S Wainer (cds.) Proof Theory, Cambridge University Press, 1992, in press. c.
 J V Tucker and J I Zucker, Algebraic specifications of generalised computable functions over abstract data types, in preparation.
 J V Tucker, J I Zucker, and K Meinke, Computability on abstract structures, in S. Abramsky, D. Gabbay and T Maibaum (eds.) Handbook of Logic for Computer Science, Oxford University Press, in preparation.
 W Wechler, Universal Algebra for Computer Scientists, EATCS Monographs, Springer Verlag, Berlin, 1991.
 M Wirsing, Algebraic specification, in J van Leeuwen (ed) Handbook of Theoretical Computer Science. Volume B: Formal Models and Semantics, Elsevier, 1990, pp. 675–788.
 Title
 Theory of computation over stream algebras, and its applications
 Book Title
 Mathematical Foundations of Computer Science 1992
 Book Subtitle
 17th International Symposium Prague, Czechoslovakia, August 24–28, 1992 Proceedings
 Pages
 pp 6280
 Copyright
 1992
 DOI
 10.1007/354055808X_6
 Print ISBN
 9783540558088
 Online ISBN
 9783540472919
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 629
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors
 Authors

 J. V. Tucker ^{(1)}
 J. I. Zucker ^{(2)}
 Author Affiliations

 1. Department of Mathematics and Computer Science, University College of Swansea, SA2 8PP, Singleton Park, Swansea, Wales
 2. Department of Computer Science, McMaster University, L8S 4K1, Hamilton, Ontario, Canada
Continue reading...
To view the rest of this content please follow the download PDF link above.