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Universality and semicomputability for nondeterministic programming languages over abstract algebras

Wei Jiang, Yuan Wang, Jeffery Zucker
2007 The Journal of Logic and Algebraic Programming  
There are two topics of investigation: (1) the extent to which the UFT holds over abstract algebras in these languages; (2) concepts of semicomputability for these languages, and the extent to which they  ...  Classical computability theory, including the UFT and the theory of semicomputable sets, has been extended by Tucker and Zucker to abstract many-sorted algebras, with algorithms formalized as deterministic  ...  Acknowledgements This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada. We thank an anonymous referee for helpful suggestions. Appendix A.  ... 
doi:10.1016/j.jlap.2006.09.001 fatcat:5r7u2nkfjzcwdj23wa2etmo2vy

Generalizing Computability Theory to Abstract Algebras [chapter]

J. V. Tucker, J. I. Zucker
2015 Turing's Revolution  
We also thank the editors, Giovanni Sommaruga and Thomas Strahm, for the opportunity to participate in this volume, and for their helpfulness during the preparation of this chapter.  ...  We are grateful to Mark Armstrong, Sol Feferman, Diogo Poças and an anonymous referee for very helpful comments on earlier drafts of this chapter.  ...  We will see that For any given Σ-algebra A, there is a universal While procedure over A if, and only if, there is a While program for term evaluation over A.  ... 
doi:10.1007/978-3-319-22156-4_5 fatcat:bj42pmzvjzedjkmtgpvuswn64u

Deterministic and nondeterministic computation, and horn programs, on abstract data types

J.V. Tucker, J.I. Zucker
1992 The Journal of Logic Programming  
Two characterizations are considered and shown to be equivalent: one in terms of " partial computable functions' ' (for a suitable notion of computability over abstract structures) and one in terms of  ...  definability by means of Horn programs over such structures.  ...  Derrick and M. Fairtlough (Leeds) for valuable discussions, and J.-L. Lassez for inviting us to give a detailed exposition of these results.  ... 
doi:10.1016/0743-1066(92)90020-4 fatcat:ghcujd36yzaebmrd33x6yfy6by


1991 International Journal of Foundations of Computer Science  
We consider projections of semicomputable relations on abstract structures We show that they arise in several contexts, including nondeterministic extensions of while' programs with arrays by means of  ...  An important technique in this investigation is the study of computation trees for imperative programs, in order to prove characterization theorems for semicomputable sets, of a form rst developed by E  ...  We thank an anonymous referee for constructive suggestions.  ... 
doi:10.1142/s0129054191000170 fatcat:sqxfm5obubbs7k35f3fw4sblfu

On the power of algebraic specifications [chapter]

J. A. Bergstra, M. Broy, J. V. Tucker, M. Wirsing
1981 Lecture Notes in Computer Science  
Finally we give an example of the specification of a simple nondeterministic programming language.  ...  For partial abstract types we prove that every computable partial algebra has an equational hidden enrichment specification and discuss the power of hierarchical partial algebras.  ...  The results for arithmetical and hyperarithmetical algebras carry over, too. Finally we consider a simple nondeterminlstlc programmlnq language.  ... 
doi:10.1007/3-540-10856-4_85 fatcat:3jcr4kf4jzfirmx44d5ow3cbdm

Page 5369 of Mathematical Reviews Vol. , Issue 90I [page]

1990 Mathematical Reviews  
, Andrzej Tarlecki and Martin Wirsing, Algebraic specifications of reachable higher-order algebras (pp. 154-169); Tobias Nipkow, Observing nondeterministic data types (pp. 170-183); Ma.  ...  Forsgren, A proof system for type theory and CCS (pp. 539- 540); Thomas Wolff, Implementation of a transition semantics for parallel programs with shared variables (pp. 541-543).  ... 

Abstract versus Concrete Computation on Metric Partial Algebras [article]

J.V. Tucker and J.I. Zucker (McMaster University, Hamilton, Canada)
2001 arXiv   pre-print
A model of computation is abstract if, when applied to any algebra, the resulting programs for computable functions and sets on that algebra are invariant under isomorphisms, and hence do not depend on  ...  We investigate the relationship between abstract and concrete models of partial metric algebras.  ...  Then we choose the ' while'-array programming language as an abstract model for computing on any data type, and extend it with a nondeterministic assignment of "countable choice".  ... 
arXiv:cs/0108007v1 fatcat:hijja3curjbs5f2b46ra73oihe

Algebraic approaches to nondeterminism---an overview

Michał Walicki, Sigurd Meldal
1997 ACM Computing Surveys  
Noncontinuity may also arise in a determinate language, for instance, in a language admitting quantification over infinite sets Broy 1983 ].  ...  In particular, the introduction of nondeterminism as a result of abstraction from time is usually taken as a given in the process algebra community without thereby necessarily accepting abstraction over  ... 
doi:10.1145/248621.248623 fatcat:5o2gkoijefg7dgznddcqefpkbi

Reference list of indexed articles

1999 Theoretical Computer Science  
Pair, Abstract data types and algebraic semantics of programming languages 18 (1) (1982) 1-31 373. J. more economical 18 (1) (1982) 33-10 374. A.P.  ...  Bergstra and J.V. Tucker, Algebraic specifications of computable and semicomputable data types 50 (2) (1987) 137-181 975. J.  ... 
doi:10.1016/s0304-3975(98)00320-x fatcat:bdgg2ekzdjahdo7g2gtwbdye6m

Cumulative index volumes 1–100

1992 Theoretical Computer Science  
Pair, A systematic study of models of abstract data types 33 (2-3) (1984) 137-174 Broy, M., On the Herbrand-Kleene universe for nondeterministic computations 36 ( 1) ( 1985) I- 19 Broy, M., A theory  ...  On the existence of free models in abstract algebraic institutions 37 (3) ( 1985) , R.D. and J.K.  ... 
doi:10.1016/0304-3975(92)90292-n fatcat:ekwes6owtrco3lkfkiqagnketq

Thermodynamic costs of Turing Machines [article]

Artemy Kolchinsky, David H. Wolpert
2020 arXiv   pre-print
For universal TMs, we show for both realizations that the thermodynamic complexity of any desired output is bounded by a constant (unlike the conventional Kolmogorov complexity), while the expected amount  ...  Turing Machines (TMs) are the canonical model of computation in computer science and physics.  ...  Tracey for many stimulating discussions, and the Santa Fe Institute for helping to support this research. This paper was made possible through the sup-  ... 
arXiv:1912.04685v3 fatcat:atjsbzkrmjb73mqksbrj7f3fly

Abstracts of Current Computer Literature

1969 IEEE transactions on computers  
60 Programs 6692 Comparison Between SIMULA and FORTRAN for Military Simulation 6696 Outer and Inner Syntax of Programming Languages 6697 TREET List Processing Languages 6699 -see also Languages  ...  Data Flow of Programs During Compilation 6695 -see also Programming Languages 490 ABSTRACTS OF CURRENT COMPUTER LITERATURE Complexity Complexities of Realization of Boolean Functions by Automata  ... 
doi:10.1109/t-c.1969.222696 fatcat:yhhpsujxdraaflgkml3euqfkxa

Nonparametric General Reinforcement Learning [article]

Jan Leike
2016 arXiv   pre-print
This undermines all existing optimality properties for AIXI.  ...  We construct a large but limit computable class containing a grain of truth and show that agents based on Thompson sampling over this class converge to play Nash equilibria in arbitrary unknown computable  ...  Introduction attempt will be made to find how to make machines use language, form abstractions and concepts, solve kinds of problems now reserved for humans, and improve themselves.  ... 
arXiv:1611.08944v1 fatcat:qaagmvpfbfecdessxa65b7d7n4

From Total Equational to Partial First-Order Logic [chapter]

Maura Cerioli, Till Mossakowski, Horst Reichel
1999 Algebraic Foundations of Systems Specification  
Alternatives to partiality, like (variants of) error algebras and order-sortedness are also discussed, showing their uses and limitations.  ...  Moreover, both the total and the partial (positive) conditional fragment are investigated in detail, and in particular the existence of initial (free) models for such restricted logical paradigms is proved  ...  Note that partial recursive functions without recursive domain are needed, for instance, whenever describing the semantics of (universal) programming languages.  ... 
doi:10.1007/978-3-642-59851-7_3 dblp:series/ifip/CerioliMR99 fatcat:wc6hrxmtcngh3pjvghj5cpomum

Where Do New Ideas Come From? How Do They Emerge? Epistemology as Computation (Information Processing) [chapter]

Gordana Dodig-Crnkovic
2007 Randomness and Complexity, From Leibniz to Chaitin  
Uspenskij. 7 Chaitin's contributions-spanning over four decades-on plain and program-size complexity, algorithmic randomness (finite and infinite sequences), applications to Gödel incompleteness, and concrete  ...  versions of AIT (hands-on programming), are central for the field.  ...  Fuchs for their invitation to join respectively the Fuzzy Sets Research Group and the Philosophy of Science Group at the Production Engineering Program, COPPE-UFRJ.  ... 
doi:10.1142/9789812770837_0015 fatcat:hhtjs3z765chpebraxckg3p4hu
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