
TL;DR
This paper explores the computational properties and limitations of Practical Regular Expressions (PRE), including simulation models, complexity results, and hierarchies, revealing both their expressive power and computational challenges.
Contribution
It introduces new simulation models, improves complexity bounds, and establishes hierarchies and decidability results for PRE with back references.
Findings
PRE can be simulated by nondeterministic finite automata with sensing heads.
Matching PRE with n variables can be done in O(n log m) space, improving previous bounds.
Matching PRE without star over a single-letter alphabet is NP-complete.
Abstract
We report on simulation, hierarchy, and decidability results for Practical Regular Expressions (PRE), which may include back references in addition to the standard operations union, concatenation, and star. The following results are obtained: PRE can be simulated by the classical model of nondeterministic finite automata with sensing one-way heads. The number of heads depends on the number of different variables in the expressions. A space bound O(n log m) for matching a text of length m with a PRE with n variables based on the previous simulation. This improves the bound O(nm) from (C\^ampeanu and Santean 2009). PRE cannot be simulated by deterministic finite automata with at most three sensing one-way heads or deterministic finite automata with any number of non-sensing one-way heads. PRE with a bounded number of occurrences of variables in any match can be simulated by…
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression · DNA and Biological Computing
