Results 21  30
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58
Undecidable properties of finite sets of equations
 J. Symbolic Logic
, 1976
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JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Association for Symbolic Logic is collaborating with JSTOR to digitize, preserve and extend access to The
RZ: A tool for bringing constructive and computable mathematics closer to programming practice
 CiE 2007: Computation and Logic in the Real World, volume 4497 of LNCS
, 2007
"... Abstract. Realizability theory can produce code interfaces for the data structure corresponding to a mathematical theory. Our tool, called RZ, serves as a bridge between constructive mathematics and programming by translating specifications in constructive logic into annotated interface code in Obje ..."
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Abstract. Realizability theory can produce code interfaces for the data structure corresponding to a mathematical theory. Our tool, called RZ, serves as a bridge between constructive mathematics and programming by translating specifications in constructive logic into annotated interface code in Objective Caml. The system supports a rich input language allowing descriptions of complex mathematical structures. RZ does not extract code from proofs, but allows any implementation method, from handwritten code to code extracted from proofs by other tools. 1
On Termination of One Rule Rewrite Systems
 Theoretical Computer Science
, 1994
"... this paper we reduce the problem of termination of one rule rewrite systems to problems somewhat more related to rewrite systems namely to Post correspondence problems and to termination of semiThue systems. Proofs we obtain this way are shorter and we expect other interesting applications from the ..."
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this paper we reduce the problem of termination of one rule rewrite systems to problems somewhat more related to rewrite systems namely to Post correspondence problems and to termination of semiThue systems. Proofs we obtain this way are shorter and we expect other interesting applications from these codings. In particular, the second part proposes a simulation of semiThue systems by one rule systems. Reduction of the termination of one rule rewrite systems to Post's correspondence problem
Turing Oracle Machines, Online Computing, and Three Displacements in Computability Theory
, 2009
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E.: Metamorphism, formal grammars and undecidable code mutation
 J. Comp. Sci
, 2007
"... Abstract — This paper presents a formalisation of the different existing code mutation techniques (polymorphism and metamorphism) by means of formal grammars. While very few theoretical results are known about the detection complexity of viral mutation techniques, we exhaustively address this critic ..."
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Abstract — This paper presents a formalisation of the different existing code mutation techniques (polymorphism and metamorphism) by means of formal grammars. While very few theoretical results are known about the detection complexity of viral mutation techniques, we exhaustively address this critical issue by considering the Chomsky classification of formal grammars. This enables us to determine which family of code mutation techniques are likely to be detected or on the contrary are bound to remain undetected. As an illustration we then present, on a formal basis, a proofofconcept metamorphic mutation engine denoted PB MOT, whose detection has been proven to be undecidable.
DECIDABILITY AND COMPLEXITY IN AUTOMATIC MONOIDS
 INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
"... Several complexity and decidability results for automatic monoids are shown: (i) there exists an automatic monoid with a Pcomplete word problem, (ii) there exists an automatic monoid such that the firstorder theory of the corresponding Cayleygraph is not elementary decidable, and (iii) there exis ..."
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Several complexity and decidability results for automatic monoids are shown: (i) there exists an automatic monoid with a Pcomplete word problem, (ii) there exists an automatic monoid such that the firstorder theory of the corresponding Cayleygraph is not elementary decidable, and (iii) there exists an automatic monoid such that reachability in the corresponding Cayleygraph is undecidable. Moreover, it is shown that for every hyperbolic group the word problem belongs to LOGCFL, which improves a result of Cai [8].
A variety with solvable, but not uniformly solvable, word problem
 Proc. London Math. Soc
, 1993
"... Dedicated, by her coauthors, to the memory of Evelyn Nelson who died after the paper was submitted Dedicated by Saharon Shelah to his friend Alan Mekler In the literature two notions of the word problem for a variety occur. A variety has a decidable word problem if every finitely presented algebra ..."
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Dedicated, by her coauthors, to the memory of Evelyn Nelson who died after the paper was submitted Dedicated by Saharon Shelah to his friend Alan Mekler In the literature two notions of the word problem for a variety occur. A variety has a decidable word problem if every finitely presented algebra in the variety has a decidable word problem. It has a uniformly decidable word problem if there is an algorithm which given a finite presentation produces an algorithm for solving the word problem of the algebra so presented. A variety is given with finitely many axioms having a decidable, but not uniformly decidable, word problem. Other related examples are given as well. The following two options occur in the literature for what is meant by the solvability of the word problem for a variety V: (1) there is an algorithm which, given a finite presentation 9 * in finitely many generators and relations, solves the word problem for 9 relative to the
Implementing real numbers with RZ
, 2007
"... RZ is a tool which translates axiomatizations of mathematical structures to program specifications using the realizability interpretation of logic. This helps programmers correctly implement data structures for computable mathematics. RZ does not prescribe a particular method of implementation, but ..."
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RZ is a tool which translates axiomatizations of mathematical structures to program specifications using the realizability interpretation of logic. This helps programmers correctly implement data structures for computable mathematics. RZ does not prescribe a particular method of implementation, but allows programmers to write efficient code by hand, or to extract trusted code from formal proofs, if they so desire. We used this methodology to axiomatize real numbers and implemented the specification computed by RZ. The axiomatization is the standard domaintheoretic construction of reals as the maximal elements of the interval domain, while the implementation closely follows current stateoftheart implementations of exact real arithmetic. Our results shows not only that the theory and practice of computable mathematics can coexist, but also that they work together harmoniously.
Type Inference for Recursive Definitions
 In Proc. 14th Ann. IEEE Symp. Logic in Comput. Sci
, 2000
"... We consider type systems that combine universal types, recursive types, and object types. We study type inference in these systems under a rank restriction, following Leivant's notion of rank. To motivate our work, we present several examples showing how our systems can be used to type programs enco ..."
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We consider type systems that combine universal types, recursive types, and object types. We study type inference in these systems under a rank restriction, following Leivant's notion of rank. To motivate our work, we present several examples showing how our systems can be used to type programs encountered in practice. We show that type inference in the rankk system is decidable for k # 2 and undecidable for k # 3. (Similar results based on different techniques are known to hold for System F, without recursive types and object types.) Our undecidability result is obtained by a reduction from a particular adaptation (which we call "regular") of the semiunification problem and whose undecidability is, interestingly, obtained by methods totally different from those used in the case of standard (or finite) semiunification. Keywords: type systems, type inference, lambda calculus, unification, software specification. 1 Introduction 1.1 Background and Motivation Type inference, the ...
An algebraic characterization of the halting probability
 FUNDAMENTA INFORMATICAE
, 2007
"... Using 1947 work of Post showing that the word problem for semigroups is unsolvable, we explicitly exhibit an algebraic characterization of the bits of the halting probability Ω. Our proof closely follows a 1978 formulation of Post’s work by M. Davis. The proof is selfcontained and not very complicat ..."
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Using 1947 work of Post showing that the word problem for semigroups is unsolvable, we explicitly exhibit an algebraic characterization of the bits of the halting probability Ω. Our proof closely follows a 1978 formulation of Post’s work by M. Davis. The proof is selfcontained and not very complicated.