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On SRegular PrefixRewriting Systems and Automatic Structures
 Computing and Combinatorics, Proceedings COCOON'99, Lecture Notes in Computer Science 1627
, 1998
"... Underlying the notion of an automatic structure is that of a synchronously regular (sregular for short) set of pairs of strings. Accordingly we consider sregular prefixrewriting systems showing that even for fairly restricted systems of this form confluence is undecidable in general. Then a close ..."
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Underlying the notion of an automatic structure is that of a synchronously regular (sregular for short) set of pairs of strings. Accordingly we consider sregular prefixrewriting systems showing that even for fairly restricted systems of this form confluence is undecidable in general. Then a close correspondence is established between the existence of an automatic structure that yields a prefixclosed set of unique representatives for a finitely generated monoid and the existence of an sregular canonical prefixrewriting system presenting that monoid. Keywords: prefixrewriting system, regularity preservation, confluence, monoidpresentation, automatic structure. 1 Introduction A fundamental issue in computational algebra is the quest for classes of finite descriptions of infinite algebraic structures such that these descriptions allow algorithmic solutions for various decision problems. In the case of monoids and groups, infinite structures can be presented through finite presenta...
Markov semigroups, monoids, and groups
, 2011
"... A group is Markov if it admits a prefixclosed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimallength representatives over every generating set. This paper considers the natural generalizations of thes ..."
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A group is Markov if it admits a prefixclosed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimallength representatives over every generating set. This paper considers the natural generalizations of these concepts to semigroups and monoids. Two distinct potential generalizations to monoids are shown to be equivalent. Various interesting examples are presented, including an example of a nonMarkov monoid that nevertheless admits a regular language of unique representatives over any generating set. It is shown that all finitely generated commutative semigroups are strongly Markov, but that finitely generated subsemigroups of virtually abelian or polycyclic groups need not be. Potential connections with wordhyperbolic semigroups are investigated. A study is made of the interaction of the classes of Markov and strongly Markov semigroups with direct products, free products, and finiteindex subsemigroups and extensions. Several questions are posed.
Finitely presented monoids with linear Dehn function need not have regular crosssections. Semigroup Forum (to appear
"... abstract This paper shows that a finitely presented monoid with linear Dehn function need not have a regular crosssection, strengthening the previouslyknown result that such a monoid need not be presented by a finite complete string rewriting system, and contrasting with the fact that finitely pr ..."
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abstract This paper shows that a finitely presented monoid with linear Dehn function need not have a regular crosssection, strengthening the previouslyknown result that such a monoid need not be presented by a finite complete string rewriting system, and contrasting with the fact that finitely presented groups with linear Dehn function always have regular crosssections.
unknown title
"... The use of isoperimetric and Dehn functions in group theory stems from the seminal paper of Gromov [8] and its characterization of wordhyperbolic groups as groups having linear Dehn functions. Another characterization of wordhyperbolic groups is admitting a Dehn presentation (equivalently, a prese ..."
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The use of isoperimetric and Dehn functions in group theory stems from the seminal paper of Gromov [8] and its characterization of wordhyperbolic groups as groups having linear Dehn functions. Another characterization of wordhyperbolic groups is admitting a Dehn presentation (equivalently, a presentation via a finite
A Survey on the Computational Power of Some Classes of Finite MonoidPresentations
, 1998
"... An overview is given on the decidability results that have been obtained for the various classes of finite monoidpresentations that involve stringrewriting systems which are noetherian and (weakly) confluent. Further, the KnuthBendix completion procedure and some of its extensions are described. ..."
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An overview is given on the decidability results that have been obtained for the various classes of finite monoidpresentations that involve stringrewriting systems which are noetherian and (weakly) confluent. Further, the KnuthBendix completion procedure and some of its extensions are described. Finally, a current research project supported by the Deutsche Forschungsgemeinschaft (DFG) is presented that aims at the development of a software system XSSR that realizes the various decidability results presented in the paper. 1 Introduction One of the forerunners of modern computational algebra is certainly its subfield of computational group theory, which today is being extended to computational semigroup theory. Not just results on the algebraic structure of a (semi) group are of interest any more, but emphasis is being placed on actually solving algorithmic problems for (semi) groups, that is, one is interested in effectively performing computations with the elements of a (semi) ...
Lexicalized RRWWAutomata – A New Measure for The Degree of Nondeterminism of (ContextFree) Languages ∗
, 2007
"... Restarting automata can be seen as analytical variants of classical automata as well as of regulated rewriting systems. We study a measure for the degree of nondeterminism of (contextfree) languages in terms of deterministic restarting automata that are (strongly) lexicalized. This measure is based ..."
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Restarting automata can be seen as analytical variants of classical automata as well as of regulated rewriting systems. We study a measure for the degree of nondeterminism of (contextfree) languages in terms of deterministic restarting automata that are (strongly) lexicalized. This measure is based on the number of auxiliary symbols (categories)