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Properties of Monoids That Are Presented By Finite Convergent StringRewriting Systems  a Survey
, 1997
"... In recent years a number of conditions has been established that a monoid must necessarily satisfy if it is to have a presentation through some finite convergent stringrewriting system. Here we give a survey on this development, explaining these necessary conditions in detail and describing the rela ..."
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In recent years a number of conditions has been established that a monoid must necessarily satisfy if it is to have a presentation through some finite convergent stringrewriting system. Here we give a survey on this development, explaining these necessary conditions in detail and describing the relationships between them. 1 Introduction Stringrewriting systems, also known as semiThue systems, have played a major role in the development of theoretical computer science. On the one hand, they give a calculus that is equivalent to that of the Turing machine (see, e.g., [Dav58]), and in this way they capture the notion of `effective computability' that is central to computer science. On the other hand, in the phrasestructure grammars introduced by N. Chomsky they are used as sets of productions, which form the essential part of these grammars [HoUl79]. In this way stringrewriting systems are at the very heart of formal language theory. Finally, they are also used in combinatorial semig...
On the Expressive Power of Existential Quantification in PolynomialTime Computability
"... this paper to study the expressive power of bounded existential quantification in polynomialtime computability. Our goal was to characterize nondeterministic polynomialtime computations in a machineindependent way. The following considerations are intended to make our idea clear. Let # be the fin ..."
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this paper to study the expressive power of bounded existential quantification in polynomialtime computability. Our goal was to characterize nondeterministic polynomialtime computations in a machineindependent way. The following considerations are intended to make our idea clear. Let # be the finite alphabet
Conditional semiThue Systems for Presenting Monoids
 PROC. STACS'92
, 1992
"... There are well known examples of monoids in literature which do not admit a finite and canonical presentation by a semiThue system over a fixed alphabet, not even over an arbitrary alphabet. We introduce conditional Thue and semiThue systems similar to conditional term rewriting systems as defined ..."
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There are well known examples of monoids in literature which do not admit a finite and canonical presentation by a semiThue system over a fixed alphabet, not even over an arbitrary alphabet. We introduce conditional Thue and semiThue systems similar to conditional term rewriting systems as defined by Kaplan. Using these conditional semiThue systems we give finite and canonical presentations of the examples mentioned above. Furthermore we show, that each finitely generated monoid with decidable word problem is embeddable in a monoid which has a finite canonical conditional presentation.