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102
The word problem for cancellation semigroups with zero
 JOURNAL OF SYMBOLIC LOGIC
, 1984
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The origins of combinatorics on words
, 2007
"... We investigate the historical roots of the field of combinatorics on words. They comprise applications and interpretations in algebra, geometry and combinatorial enumeration. These considerations gave rise to early results such as those of Axel Thue at the beginning of the 20th century. Other early ..."
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We investigate the historical roots of the field of combinatorics on words. They comprise applications and interpretations in algebra, geometry and combinatorial enumeration. These considerations gave rise to early results such as those of Axel Thue at the beginning of the 20th century. Other early results were obtained as a byproduct of investigations on various combinatorial objects. For example, paths in graphs are encoded by words in a natural way, and conversely, the Cayley graph of a group or a semigroup encodes words by paths. We give in this text an account of this twosided interaction.
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.
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
Databases and FiniteModel Theory
 IN DESCRIPTIVE COMPLEXITY AND FINITE MODELS
, 1997
"... Databases provide one of the main concrete scenarios for finitemodel theory within computer science. This paper presents an informal overview of database theory aimed at finitemodel theorists, emphasizing the specificity of the database area. It is argued that the area of databases is a rich sourc ..."
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Databases provide one of the main concrete scenarios for finitemodel theory within computer science. This paper presents an informal overview of database theory aimed at finitemodel theorists, emphasizing the specificity of the database area. It is argued that the area of databases is a rich source of questions and vitality for finitemodel theory.
Undecidable properties of finite sets of equations
 J. Symbolic Logic
, 1976
"... 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 JS ..."
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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
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].
The word problem in groups of cohomological dimension 2, from: “Groups St
 in Bath, I”, London Math. Soc. Lecture Note Ser. 260
, 1997
"... Abstract. We show that the flnitely presented groups with unsolvable word problem given by the BooneBritton construction have cohomological dimension 2. More precisely we show these groups can be obtained from a free group by successively forming HNNextensions where the associated subgroups are ..."
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Abstract. We show that the flnitely presented groups with unsolvable word problem given by the BooneBritton construction have cohomological dimension 2. More precisely we show these groups can be obtained from a free group by successively forming HNNextensions where the associated subgroups are flnitely generated free groups. Also the presentations obtained for these groups are aspherical. Using this we show there is no algorithm to determine whether a presentation is aspherical. There is no algorithm to determine whether a flnite 2complex is aspherical. 1.