Linear Compressed Pattern Matching for Polynomial Rewriting (Extended Abstract)

Manfred Schmidt-Schauss

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.

In Rachid Echahed and Detlef Plump: Proceedings 7th International Workshop on Computing with Terms and Graphs (TERMGRAPH 2013), Rome, 23th March 2013, Electronic Proceedings in Theoretical Computer Science 110, pp. 29–40.
Published: 25th February 2013.

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