Results 1  10
of
18
Axel Thue's work on repetitions in words
 Invited Lecture at the 4th Conference on Formal Power Series and Algebraic Combinatorics
, 1992
"... The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched. ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched.
Normalised Rewriting and Normalised Completion
, 1994
"... We introduce normalised rewriting, a new rewrite relation. It generalises former notions of rewriting modulo E, dropping some conditions on E. For example, E can now be the theory of identity, idempotency, the theory of Abelian groups, the theory of commutative rings. We give a new completion algor ..."
Abstract

Cited by 19 (2 self)
 Add to MetaCart
We introduce normalised rewriting, a new rewrite relation. It generalises former notions of rewriting modulo E, dropping some conditions on E. For example, E can now be the theory of identity, idempotency, the theory of Abelian groups, the theory of commutative rings. We give a new completion algorithm for normalised rewriting. It contains as an instance the usual AC completion algorithm, but also the wellknown Buchberger's algorithm for computing standard bases of polynomial ideals. We investigate the particular case of completion of ground equations, In this case we prove by a uniform method that completion modulo E terminates, for some interesting E. As a consequence, we obtain the decidability of the word problem for some classes of equational theories. We give implementation results which shows the efficiency of normalised completion with respect to completion modulo AC. 1 Introduction Equational axioms are very common in most sciences, including computer science. Equations can ...
Normal Monomodal Logics Can Simulate All Others
 Journal of Symbolic Logic
, 1999
"... This paper shows that nonnormal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
This paper shows that nonnormal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic. Normal monomodal logics can simulate all others 1 This paper is dedicated to our teacher, Wolfgang Rautenberg x1. Introduction. A simulation of a logic by a logic \Theta is a translation of the expressions of the language for into the language of \Theta such that the consequence relation defined by is reflected under the translation by the consequence relation of \Theta. A wellknown case is provided by the Godel translation, which simulates intuitionistic logic by Grzegorczyk's logic (cf. [11] and [5]). Such simulations not only yield technical results but may also ...
Algorithmic problems in groups, semigroups and inverse semigroups
 Semigroups, Formal Languages and Groups
, 1995
"... ..."
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 ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
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
All Countable Monoids Embed into the Monoid of the Infinite Random Graph
"... We prove that the endomorphism monoid of the infinite random graph R contains as a submonoid an isomorphic copy of each countable monoid. As a corollary, the monoid of R does not satisfy any nontrivial semigroup identity. We also prove that the full transformation monoid on a countably infinite ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We prove that the endomorphism monoid of the infinite random graph R contains as a submonoid an isomorphic copy of each countable monoid. As a corollary, the monoid of R does not satisfy any nontrivial semigroup identity. We also prove that the full transformation monoid on a countably infinite set is isomorphic to a submonoid of the monoid of R.
Word Problems for 2Homogeneous Monoids and Symmetric Logspace
 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science (MFCS 2001), Marianske Lazne (Czech Republic), number 2136 in Lecture Notes in Computer Science
, 2001
"... We prove that the word problem for every monoid presented by a fixed 2homogeneous semiThue system can be solved in logspace, which generalizes a result of Lipton and Zalcstein for free groups. The uniform word problem for the class of all 2homogeneous semiThue systems is shown to be complete fo ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We prove that the word problem for every monoid presented by a fixed 2homogeneous semiThue system can be solved in logspace, which generalizes a result of Lipton and Zalcstein for free groups. The uniform word problem for the class of all 2homogeneous semiThue systems is shown to be complete for symmetric logspace.