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

An Environment for Analyzing Space Optimizations in Call-by-Need Functional Languages

We present an implementation of an interpreter LRPi for the call-by-need calculus LRP, based on a variant of Sestoft's abstract machine Mark 1, extended with an eager garbage collector. It is used as a tool for exact space usage analyses as a support for our investigations into space improvements of call-by-need calculi.Comment: In Proceedings WPTE 2016, arXiv:1701.0023

On the complexity of bounded second-order unification and stratified context unification

Bounded Second-Order Unification is a decidable variant of undecidable Second-Order Unification. Stratified Context Unification is a decidable restriction of Context Unification, whose decidability is a long-standing open problem. This paper is a join of two separate previous, preliminary papers on NP-completeness of Bounded Second-Order Unification and Stratified Context Unification. It clarifies some omissions in these papers, joins the algorithmic parts that construct a minimal solution, and gives a clear account of a method of using singleton tree grammars for compression that may have potential usage for other algorithmic questions in related areas. © The Author 2010. Published by Oxford University Press. All rights reserved.This research has been partially supported by the research projects Mulog-2 (TIN2007-68005-C04-01) and SuRoS TIN2008-04547) funded by the CICyTPeer Reviewe

Correctly Translating Concurrency Primitives

International audienceMotivated by the question of correctness of a specific implementation of concurrent buffers in the lambda calculus with futures underlying Alice ML, we prove that concurrent buffers and handled futures can correctly encode each other. Correctness means that our encodings preserve and reflect the observations of may- and must-convergence. This also shows correctness wrt. program semantics, since the encodings are adequate translations wrt. contextual semantics. While these translations encode blocking into queuing and waiting, we also provide an adequate encoding of buffers in a calculus without handles, which is more low-level and uses busy-waiting instead of blocking. Furthermore we demonstrate that our correctness concept applies to the whole compilation process from high-level to low-level concurrent languages, by translating the calculus with buffers, handled futures and data constructors into a small core language without those constructs

On the Complexity of Linear and Stratified : Context Matching Problems

We give algorithms for linear and for general context matching and discuss how the performance in the general case can be improved through the use of information derived from approximations that can be computed in polynomial time. We investigate the complexity of context matching with respect to the stratification of variable occurrences, where our main results are that stratified context matching is NP-complete, but that stratified simultaneous monadic context matching is in P. SSMCM is equivalent to stratified simultaneous word matching. We also show that the linear and the shared-linear case are in P and of time complexity $O(n^3)$, and that varity 2 context matching, where variables occur at most twice, is NP-complete

Turning Informal Thesauri Into Formal Ontologies: A Feasibility Study on Biomedical Knowledge re-Use

This paper reports a large-scale knowledge conversion and curation experiment. Biomedical domain knowledge from a semantically weak and shallow terminological resource, the UMLS, is transformed into a rigorous description logics format. This way, the broad coverage of the UMLS is combined with inference mechanisms for consistency and cycle checking. They are the key to proper cleansing of the knowledge directly imported from the UMLS, as well as subsequent updating, maintenance and refinement of large knowledge repositories. The emerging biomedical knowledge base currently comprises more than 240 000 conceptual entities and hence constitutes one of the largest formal knowledge repositories ever built

Quantifier-Free Interpolation of a Theory of Arrays

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifier- free interpolants in general. In this paper, we show that it is possible to obtain quantifier-free interpolants for a Skolemized version of the extensional theory of arrays. We prove this in two ways: (1) non-constructively, by using the model theoretic notion of amalgamation, which is known to be equivalent to admit quantifier-free interpolation for universal theories; and (2) constructively, by designing an interpolating procedure, based on solving equations between array updates. (Interestingly, rewriting techniques are used in the key steps of the solver and its proof of correctness.) To the best of our knowledge, this is the first successful attempt of computing quantifier- free interpolants for a variant of the theory of arrays with extensionality

A Modular Order-sorted Equational Generalization Algorithm

Generalization, also called anti-unification, is the dual of unification. Given terms t and t , a generalizer is a term t of which t and t are substitution instances. The dual of a most general unifier (mgu) is that of least general generalizer (lgg). In this work, we extend the known untyped generalization algorithm to, first, an order-sorted typed setting with sorts, subsorts, and subtype polymorphism; second, we extend it to work modulo equational theories, where function symbols can obey any combination of associativity, commutativity, and identity axioms (including the empty set of such axioms); and third, to the combination of both, which results in a modular, order-sorted equational generalization algorithm. Unlike the untyped case, there is in general no single lgg in our framework, due to order-sortedness or to the equational axioms. Instead, there is a finite, minimal and complete set of lggs, so that any other generalizer has at least one of them as an instance. Our generalization algorithms are expressed by means of inference systems for which we give proofs of correctness. This opens up new applications to partial evaluation, program synthesis, and theorem proving for typed equational reasoning systems and typed rulebased languages such as ASF+SDF, Elan, OBJ, Cafe-OBJ, and Maude. © 2014 Elsevier Inc. All rights reserved. 1.M. Alpuente, S. Escobar, and J. Espert have been partially supported by the EU (FEDER) and the Spanish MEC/MICINN under grant TIN 2010-21062-C02-02, and by Generalitat Valenciana PROMETEO2011/052. J. Meseguer has been supported by NSF Grants CNS 09-04749, and CCF 09-05584.Alpuente Frasnedo, M.; Escobar Román, S.; Espert Real, J.; Meseguer, J. (2014). A Modular Order-sorted Equational Generalization Algorithm. Information and Computation. 235:98-136. https://doi.org/10.1016/j.ic.2014.01.006S9813623

Frontmatter, Table of Contents, Preface, Conference Organization

Frontmatter, Table of Contents, Preface, Conference Organizatio

Computational aspects of an order-sorted logic with term declarations

SIGLEAvailable from TIB Hannover: RO 7629(88-10) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman