Results 1  10
of
32
On the Expressivity of Feature Logics with Negation, Functional Uncertainty, and Sort Equations
 JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
, 1993
"... Feature logics are the logical basis for socalled unification grammars studied in computational linguistics. We investigate the expressivity of feature terms with negation and the functional uncertainty construct needed for the description of longdistance dependencies and obtain the following resu ..."
Abstract

Cited by 40 (12 self)
 Add to MetaCart
Feature logics are the logical basis for socalled unification grammars studied in computational linguistics. We investigate the expressivity of feature terms with negation and the functional uncertainty construct needed for the description of longdistance dependencies and obtain the following results: satisfiability of feature terms is undecidable, sort equations can be internalized, consistency of sort equations is decidable if there is at least one atom, and consistency of sort equations is undecidable if there is no atom.
Word problems and membership problems on compressed words
 SIAM J. Comput., 35(5):1210
"... Abstract. We consider a compressed form of the word problem for finitely presented monoids, where the input consists of two compressed representations of words over the generators of a monoid M, and we ask whether these two words represent the same monoid element of M. Words are compressed using str ..."
Abstract

Cited by 11 (7 self)
 Add to MetaCart
Abstract. We consider a compressed form of the word problem for finitely presented monoids, where the input consists of two compressed representations of words over the generators of a monoid M, and we ask whether these two words represent the same monoid element of M. Words are compressed using straightline programs, i.e., contextfree grammars that generate exactly one word. For several classes of finitely presented monoids we obtain completeness results for complexity classes in the range from P to EXPSPACE. As a byproduct of our results on compressed word problems we obtain a fixed deterministic contextfree language with a PSPACEcomplete compressed membership problem. The existence of such a language was open so far. Finally, we will investigate the complexity of the compressed membership problem for various circuit complexity classes. Key words. grammarbased compression, word problems for monoids, contextfree languages, complexity AMS subject classifications. 20F10, 68Q17, 68Q42
Order computations in generic groups
 PHD THESIS MIT, SUBMITTED JUNE 2007. RESOURCES
, 2007
"... ..."
Towards Open Type Functions for Haskell
"... Abstract. We report on an extension of Haskell with type(level) functions and equality constraints. We illustrate their usefulness in the context of phantom types, GADTs and type classes. Problems in the context of type checking are identified and we sketch our solution: a decidable type checking a ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
Abstract. We report on an extension of Haskell with type(level) functions and equality constraints. We illustrate their usefulness in the context of phantom types, GADTs and type classes. Problems in the context of type checking are identified and we sketch our solution: a decidable type checking algorithm for a restricted class of type functions. Moreover, functional dependencies are now obsolete: we show how they can be encoded as type functions. 1
Questions in Computable Algebra and Combinatorics
, 1999
"... this article, we will focus on two areas of computable mathematics, namely computable algebra and combinatorics. The goal of this article is to present a number of open questions in both computable algebra and computable combinatorics and to give the reader a sense of the research activity in these ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
this article, we will focus on two areas of computable mathematics, namely computable algebra and combinatorics. The goal of this article is to present a number of open questions in both computable algebra and computable combinatorics and to give the reader a sense of the research activity in these elds. Our philosophy is to try to highlight questions, whose solutions we feel will either give insight into algebra or combinatorics, or will require new technology in the computabilitytheoretical techniques needed. A good historical example of the rst phenomenom is the word problem for nitely presented groups which needed the development of a great deal of group theoretical machinery for its solution by Novikov [110] and Boone [10]. A good example of the latter phenomenon is the recent solution by Coles, Downey and Slaman [17] of the question of whether all rank one torsion free 1991 Mathematics Subject Classi cation. Primary 03D45; Secondary 03D25
KnuthBendix Completion with Modern Termination Checking

, 2006
"... KnuthBendix completion is a technique for equational automated theorem proving based on term rewriting. This classic procedure is parametrized by an equational theory and a (wellfounded) reduction order used at runtime to ensure termination of intermediate rewriting systems. Any reduction order ca ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
KnuthBendix completion is a technique for equational automated theorem proving based on term rewriting. This classic procedure is parametrized by an equational theory and a (wellfounded) reduction order used at runtime to ensure termination of intermediate rewriting systems. Any reduction order can be used in principle, but modern completion tools typically implement only a few classes of such orders (e.g., recursive path orders and polynomial orders). Consequently, the theories for which completion can possibly succeed are limited to those compatible with an instance of an implemented class of orders. Finding and specifying a compatible order, even among a small number of classes, is challenging in practice and crucial to the success of the method. In this thesis, a new variant on the KnuthBendix completion procedure is developed in which no order is provided by the user. Modern terminationchecking methods are instead used to verify termination of rewriting systems. We prove the new method correct and also present an implementation called Slothrop which obtains solutions for theories that do not admit typical orders and that have not
Finiteness conditions on subgroups and formal language theory
 Proc. London Math. Soc
, 1989
"... Dedicated to the memory of W. W. Boone We show in this article that the most usual finiteness conditions on a subgroup of a finitely generated group all have equivalent formulations in terms of formal language theory. This correspondence gives simple proofs of various theorems concerning intersectio ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Dedicated to the memory of W. W. Boone We show in this article that the most usual finiteness conditions on a subgroup of a finitely generated group all have equivalent formulations in terms of formal language theory. This correspondence gives simple proofs of various theorems concerning intersections of subgroups and the preservation of finiteness conditions in a uniform manner. We then establish easily the theorems of Greibach and of Griffiths by considering free reductions of languages that describe the computations of pushdown automata in one case and of Turing machines in the other, thus making clear that they are essentially the same. 1.