Linear Compressed Pattern Matching for Polynomial Rewriting (Extended Abstract)

This paper is an extended abstract of an analysis of term rewriting where the terms in the rewrite rules as well as the term to be rewritten are compressed by a singleton tree grammar (STG). This form of compression is more general than node sharing or representing terms as dags since also partial trees (contexts) can be shared in the compression. In the first part efficient but complex algorithms for detecting applicability of a rewrite rule under STG-compression are constructed and analyzed. The second part applies these results to term rewriting sequences. The main result for submatching is that finding a redex of a left-linear rule can be performed in polynomial time under STG-compression. The main implications for rewriting and (single-position or parallel) rewriting steps are: (i) under STG-compression, n rewriting steps can be performed in nondeterministic polynomial time. (ii) under STG-compression and for left-linear rewrite rules a sequence of n rewriting steps can be performed in polynomial time, and (iii) for compressed rewrite rules where the left hand sides are either DAG-compressed or ground and STG-compressed, and an STG-compressed target term, n rewriting steps can be performed in polynomial time.Comment: In Proceedings TERMGRAPH 2013, arXiv:1302.599

Multiple hierarchies : new aspects of an old solution

In this paper, we present the Multiple Annotation approach, which solves two problems: the problem of annotating overlapping structures, and the problem that occurs when documents should be annotated according to different, possibly heterogeneous tag sets. This approach has many advantages: it is based on XML, the modeling of alternative annotations is possible, each level can be viewed separately, and new levels can be added at any time. The files can be regarded as an interrelated unit, with the text serving as the implicit link. Two representations of the information contained in the multiple files (one in Prolog and one in XML) are described. These representations serve as a base for several applications

Operational Semantics of Resolution and Productivity in Horn Clause Logic

This paper presents a study of operational and type-theoretic properties of different resolution strategies in Horn clause logic. We distinguish four different kinds of resolution: resolution by unification (SLD-resolution), resolution by term-matching, the recently introduced structural resolution, and partial (or lazy) resolution. We express them all uniformly as abstract reduction systems, which allows us to undertake a thorough comparative analysis of their properties. To match this small-step semantics, we propose to take Howard's System H as a type-theoretic semantic counterpart. Using System H, we interpret Horn formulas as types, and a derivation for a given formula as the proof term inhabiting the type given by the formula. We prove soundness of these abstract reduction systems relative to System H, and we show completeness of SLD-resolution and structural resolution relative to System H. We identify conditions under which structural resolution is operationally equivalent to SLD-resolution. We show correspondence between term-matching resolution for Horn clause programs without existential variables and term rewriting.Comment: Journal Formal Aspect of Computing, 201

A Unification Algorithm for Second-Order Linear Terms

We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence

Unification modulo Lists with Reverse as Solving Simple Sets of Word Equations

Decision procedures for various list theories have been investigated in the literature with applications to automated verification. Here we show that the unifiability problem for some list theories with a reverse operator is NP-complete. We also give a unifiability algorithm for the case where the theories are extended with a length operator on lists

Matching in the Pi-Calculus

We study whether, in the pi-calculus, the match prefix-a conditional operator testing two names for (syntactic) equality-is expressible via the other operators. Previously, Carbone and Maffeis proved that matching is not expressible this way under rather strong requirements (preservation and reflection of observables). Later on, Gorla developed a by now widely-tested set of criteria for encodings that allows much more freedom (e.g. instead of direct translations of observables it allows comparison of calculi with respect to reachability of successful states). In this paper, we offer a considerably stronger separation result on the non-expressibility of matching using only Gorla's relaxed requirements.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127