Aspects of classical language theory
Handbook of formal languages, vol. 1
Handbook of formal languages, vol. 1
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Binary patterns in infinite binary words
Formal and natural computing
Theoretical Computer Science - The art of theory
Finite Automata, Palindromes, Powers, and Patterns
Language and Automata Theory and Applications
Detecting palindromes, patterns and borders in regular languages
Information and Computation
Hi-index | 0.00 |
A word p, over the alphabet of variables E, is a pattern of a word w over A if there exists a non-erasing morphism h from E* to A* such that h(p)=w. If we take E=A, given two words u, v ∈ A*, we write u ≤ v if u is a pattern of v. The restriction of ≤ to aA*, where A is the binary alphabet {a, b}, is a partial order relation. We introduce, given a word v, the set P(v) of all words u such that u ≤ v. P(v), with the relation ≤, is a poset and it is called the pattern poset of v. The first part of the paper is devoted to investigate the relationships between the structure of the poset P(v) and the combinatorial properties of the word v. In the last section, for a given language L, we consider the language P(L) of all patterns of words in L. The main result of this section shows that, if L is a regular language, then P(L) is a regular language too.