TY - GEN

T1 - Unification with Singleton Tree Grammars

AU - Gascón, Adria

AU - Godoy, Guillem

AU - Schmidt-Schauß, Manfred

PY - 2009

Y1 - 2009

N2 - Term unification plays an important role in many areas of computer science, especially in those related to logic. The universal mechanism of grammar-based compression for terms, in particular the so-called Singleton Tree Grammars (STG), have recently drawn considerable attention. Using STGs, terms of exponential size and height can be represented in linear space. Furthermore, the term representation by directed acyclic graphs (dags) can be efficiently simulated. The present paper is the result of an investigation on term unification and matching when the terms given as input are represented using different compression mechanisms for terms such as dags and Singleton Tree Grammars. We describe a polynomial time algorithm for context matching with dags, when the number of different context variables is fixed for the problem. For the same problem, NP-completeness is obtained when the terms are represented using the more general formalism of Singleton Tree Grammars. For first-order unification and matching polynomial time algorithms are presented, each of them improving previous results for those problems.

AB - Term unification plays an important role in many areas of computer science, especially in those related to logic. The universal mechanism of grammar-based compression for terms, in particular the so-called Singleton Tree Grammars (STG), have recently drawn considerable attention. Using STGs, terms of exponential size and height can be represented in linear space. Furthermore, the term representation by directed acyclic graphs (dags) can be efficiently simulated. The present paper is the result of an investigation on term unification and matching when the terms given as input are represented using different compression mechanisms for terms such as dags and Singleton Tree Grammars. We describe a polynomial time algorithm for context matching with dags, when the number of different context variables is fixed for the problem. For the same problem, NP-completeness is obtained when the terms are represented using the more general formalism of Singleton Tree Grammars. For first-order unification and matching polynomial time algorithms are presented, each of them improving previous results for those problems.

U2 - 10.1007/978-3-642-02348-4_26

DO - 10.1007/978-3-642-02348-4_26

M3 - Conference contribution

SN - 978-3-642-02347-7

T3 - Lecture Notes in Computer Science

SP - 365

EP - 379

BT - Rewriting Techniques and Applications

PB - Springer Berlin Heidelberg

ER -