Ralf Treinen
University of Paris-Sud
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Featured researches published by Ralf Treinen.
Journal of Logic Programming | 1994
Gert Smolka; Ralf Treinen
Abstract CFT is a new constraint system providing records as logical data structure for constraint (logic) programming. It can be seen as a generalization of the rational tree system employed in Prolog II, where finer-grained constraints are used and where subtrees are identified by keywords rather than by position. CFT is defined by a first-order structure consisting of so-called feature trees. Feature trees generalize the ordinary trees corresponding to first-order terms by having their edges labeled with field names called features. The mathematical semantics given by the feature tree structure is complemented with a logical semantics given by five axiom schemes, which we conjecture to comprise a complete axiomatization of the feature tree structure. We present a decision method for CFT, which decides entailment and disentailment between possibly existentially quantified constraints. Since CFT satisfies the independence property, our decision method can also be employed for checking the satisfiability of conjunctions of positive and negative constraints. This includes quantified negative constraints such as ∀ y ∀ z(x≠f(y,z)) . The paper also presents an idealized abstract machine processing negative and positive constraints incrementally. We argue that an optimized version of the machine can decide satisfiability and entailment in quasilinear time.
logical aspects of computational linguistics | 1998
Alexander Koller; Joachim Niehren; Ralf Treinen
Dominance constraints for finite tree structures are widely used in several areas of computational linguistics including syntax, semantics, and discourse. In this paper, we investigate algorithmic and complexity questions for dominance constraints and their first-order theory. The main result of this paper is that the satisfiability problem of dominance constraints is NP-complete. We present two NP algorithms for solving dominance constraints, which have been implemented in the concurrent constraint programming language Oz. Despite the intractability result, the more sophisticated of our algorithms performs well in an application to scope underspecification. We also show that the positive existential fragment of the first-order theory of dominance constraints is NP-complete and that the full first-order theory has non-elementary complexity.
Journal of Symbolic Computation | 1992
Ralf Treinen
Abstract We claim that the reduction of Posts Correspondence Problem to the decision problem of a theory provides a useful tool for proving undecidability of first order theories given by some interpretation. The goal of this paper is to define a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associativity and commutativity and of the theory of a partial lexicographic path ordering.
colloquium on trees in algebra and programming | 1994
Hubert Comon; Ralf Treinen
We survey recent results about ordering constraints on trees and discuss their applications. Our main interest lies in the family of recursive path orderings which enjoy the properties of being total, well-founded and compatible with the tree constructors. The paper includes some new results, in particular the undecidability of the theory of lexicographic path orderings in case of a non-unary signature.
Theoretical Computer Science | 1997
Hubert Comon; Ralf Treinen
We show, under some assumption on the signature, that the *This formula not viewable on a Text-Browser* fragment of the theory of any lexicographic path ordering is undecidable. This applies to partial and to total precedences. Our result implies in particular that the simplification rule of ordered completion is undecidable.
symposium on principles of programming languages | 2002
Zhendong Su; Alex Aiken; Joachim Niehren; Tim Priesnitz; Ralf Treinen
We investigate the first-order of subtyping constraints. We show that the first-order theory of non-structural subtyping is undecidable, and we show that in the case where all constructors are either unary or nullary, the first-order theory is decidable for both structural and non-structural subtyping. The decidability results are shown by reduction to a decision problem on tree automata. This work is a step towards resolving long-standing open problems of the decidability of entailment for non-structural subtyping.
Theoretical Computer Science | 2001
Franck Seynhaeve; Sophie Tison; Marc Tommasi; Ralf Treinen
Abstract We prove three new undecidability results for computational mechanisms over finite trees: There is a linear, ultra-shallow, noetherian and strongly confluent rewrite system R such that the ∃ ∗ ∀ ∗ -fragment of the first-order theory of one-step-rewriting by R is undecidable; the emptiness problem for tree automata with equality tests between cousins is undecidable; and the ∃ ∗ ∀ ∗ -fragment of the first-order theory of set constraints with the union operator is undecidable. The common feature of these three computational mechanisms is that they allow us to describe the set of first-order terms that represent grids. We extend our representation of grids by terms to a representation of linear two-dimensional patterns by linear terms, which allows us to transfer classical techniques on the grid to terms and thus to obtain our undecidability results.
rewriting techniques and applications | 1996
Ralf Treinen
The theory of one-step rewriting for a given rewrite system R and signature e is the first-order theory of the following structure: Its universe consists of all e-ground terms, and its only predicate is the relation “x rewrites to y in one step by R”. The structure contains no function symbols and no equality. We show that there is no algorithm deciding the ∃*∀*-fragment of this theory for an arbitrary rewrite system. The proof uses both non-linear and non-shallow rewrite rules.
foundations of software technology and theoretical computer science | 1990
Ralf Treinen
We claim that the reduction of Posts Correspondence Problem to the decision problem of a theory provides a useful tool for proving undecidability of first order theories given by an interpretation. The goal of this paper is to propose a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo AC and the theory of a partial lexicographic path ordering.
Information Processing Letters | 2000
Sophie Tison; Ralf Treinen; Joachim Niehren
We show that stratified context unification, which is one of the most expressive fragments of context unification known to be decidable, is equivalent to the satisfiability problem of slightly generalized rewriting constraints.