Boundary sets of regular and context-free languages
| Autor: | Sebastian Jakobi, Markus Holzer |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
060201 languages & linguistics
Discrete mathematics TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES Nested word General Computer Science Context-free language Abstract family of languages Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 06 humanities and the arts 02 engineering and technology Cone (formal languages) Pumping lemma for regular languages Theoretical Computer Science Combinatorics Deterministic finite automaton Regular language 0602 languages and literature 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Nondeterministic finite automaton Computer Science::Formal Languages and Automata Theory Mathematics |
| Zdroj: | Theoretical Computer Science. 610:59-77 |
| ISSN: | 0304-3975 |
| DOI: | 10.1016/j.tcs.2015.07.032 |
| Popis: | We investigate the descriptional and computational complexity of boundary sets of regular and context-free languages. For a letter a, the right (left, respectively) a-boundary set of a language L consists of the words in L whose a-predecessor or a-successor w.r.t. the prefix (suffix, respectively) relation is not in L. For regular languages described by deterministic finite automata (DFAs) we give tight bounds on the number of states for accepting boundary sets. Moreover, the question whether the boundary sets of a regular language is finite is shown to be NL -complete for DFAs, while it turns out to be PSPACE -complete for nondeterministic devices. Boundary sets for context-free languages are not necessarily context free anymore. Here we find a subtle difference of right and left a-boundary sets. While right a-boundary sets of deterministic context-free languages stay deterministic context free, we give an example of a deterministic context-free language whose a-boundary set is already non-context free. In fact, the finiteness problem for a-boundary sets of context-free languages becomes undecidable. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect