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Confluence of shallow rightlinear rewrite systems
 Proc. 14th CSL
, 2005
"... Abstract. We show that confluence of shallow and rightlinear term rewriting systems is decidable. This class of rewriting system is expressive enough to include nontrivial nonground rules such as commutativity, identity, and idempotence. Our proof uses the fact that this class of rewrite systems is ..."
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Cited by 10 (3 self)
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Abstract. We show that confluence of shallow and rightlinear term rewriting systems is decidable. This class of rewriting system is expressive enough to include nontrivial nonground rules such as commutativity, identity, and idempotence. Our proof uses the fact that this class of rewrite systems is known to be regularitypreserving, which implies that its reachability and joinability problems are decidable. The new decidability result is obtained by building upon our prior work for the class of ground term rewriting systems and shallow linear term rewriting systems. The proof relies on the concept of extracting more general rewrite derivations from a given rewrite derivation. 1
Parallelizing Functional Programs by Generalization
 Journal of Functional Programming
, 1997
"... List homomorphisms are functions that are parallelizable using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential ..."
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Cited by 8 (1 self)
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List homomorphisms are functions that are parallelizable using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential representations of a function, based on cons and snoclists, respectively, there is also a representation as a homomorphism. Our contribution is a mechanizable method to extract the homomorphism representation from a pair of sequential representations. The method is decomposed to a generalization problem and an inductive claim, both solvable by term rewriting techniques. To solve the former we present a sound generalization procedure which yields the required representation, and terminates under reasonable assumptions. We illustrate the method and the procedure by the parallelization of the scanfunction (parallel prefix). The inductive claim is provable automatically.
A Strict Border for the Decidability of EUnification for Recursive Functions
, 1998
"... During the execution of functional logic programs, Eunification problems have to be solved quite frequently, where the underlying equational theory is induced by recursive functions. But, what about the decidability of those Eunification problems? Up to now, there does not exist a concrete answer ..."
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Cited by 3 (0 self)
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During the execution of functional logic programs, Eunification problems have to be solved quite frequently, where the underlying equational theory is induced by recursive functions. But, what about the decidability of those Eunification problems? Up to now, there does not exist a concrete answer to this question for classes of equational theories which are induced by particular recursive functions. In this paper, we try to give an answer to this question by drawing and verifying a strict border between undecidability and decidability of Eunification problems for particular classes of recursive functions. Since this result shows that the Eunification problem is undecidable even for a very restricted class of recursive functions, the nondeterministic implementations of those problems in functional logic programming languages are justified.
Abstraction and Performance in the Design of Parallel Programs
, 1997
"... ion and Performance in the Design of Parallel Programs Der Fakultat fur Mathematik und Informatik der Universitat Passau vorgelegte Zusammenfassung der Veroffentlichungen zur Erlangung der venia legendi von Dr. Sergei Gorlatch Passau, Juli 1997 Contents 1 Introduction 2 2 Outline of the SA ..."
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Cited by 2 (0 self)
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ion and Performance in the Design of Parallel Programs Der Fakultat fur Mathematik und Informatik der Universitat Passau vorgelegte Zusammenfassung der Veroffentlichungen zur Erlangung der venia legendi von Dr. Sergei Gorlatch Passau, Juli 1997 Contents 1 Introduction 2 2 Outline of the SAT Approach 6 2.1 Performance View . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Abstraction View . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Design in SAT: Stages and Transformations . . . . . . . . . . 9 2.4 SAT and Homomorphisms . . . . . . . . . . . . . . . . . . . . 11 3 List Homomorphisms 12 4 Extraction and Adjustment 14 4.1 The CSMethod . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Mechanizing the CSMethod . . . . . . . . . . . . . . . . . . . 17 4.3 AlmostHomomorphisms: the MSS Problem . . . . . . . . . . 19 5 Composition of Homomorphisms 21 5.1 Rules of Composition . . . . . . . . . . . . . . . . . . . . . . . 21 5.2 Derivation by Transformation...
Parallelizing Functional Programs by Term Rewriting
, 1997
"... List homomorphisms are functions that can be computed in parallel using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward se ..."
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Cited by 2 (2 self)
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List homomorphisms are functions that can be computed in parallel using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential representations of a function, based on cons and snoclists, respectively, there is also a representation as a homomorphism. Our contribution is a mechanizable method to extract the homomorphism representation from a pair of sequential representations. The method is decomposed to a generalization problem and an inductive claim, both solvable by term rewriting techniques. To solve the former we present a sound generalization procedure which yields the required representation, and terminates under reasonable assumptions. We illustrate the method and the procedure by the parallelization of the scanfunction (parallel prefix). The inductive claim is provable automatically. Keywords: P...
Ezy Mnogo'sciowe W Pewnych Teoriach R'owno'sciowych
"... . Set constraints are relations between sets of ground terms over a given alphabet. They give a natural formalism for many problems in program analysis, type inference, ordersorted unification, constraint logic programming. In this paper we start studies of set constraints in the environment given ..."
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. Set constraints are relations between sets of ground terms over a given alphabet. They give a natural formalism for many problems in program analysis, type inference, ordersorted unification, constraint logic programming. In this paper we start studies of set constraints in the environment given by equational specifications. We show that in case of associativity (i.e., in free monoids) as well as in case of associativity and commutativity (i.e., in commutative monoids) the problem of consistency of systems of set constraints is undecidable; in linear nonerasing shallow theories the consistency of systems of positive set constraints is NEXPTIMEcomplete and in linear shallow theories the problem for positive and negative set constraints is decidable. Contents 1 Introduction 4 1.1 Set constraints : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.2 Earlier results : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 Definite and positive...
DECIDABLE CLASSES OF TREE AUTOMATA MIXING LOCAL AND GLOBAL CONSTRAINTS MODULO FLAT THEORIES ∗
, 2012
"... Vol. 9(2:01)2013, pp. 1–39 www.lmcsonline.org ..."