Regular and context-free pattern languages over small alphabets

Pattern languages are generalisations of the copy language, which is a standard textbook example of a context-sensitive and non-context-free language. In this work, we investigate a counter-intuitive phenomenon: with respect to alphabets of size 2 and 3, pattern languages can be regular or context-free in an unexpected way. For this regularity and context-freeness of pattern languages, we give several sufficient and necessary conditions and improve known results

Regular and context-free pattern languages over small alphabets

Pattern languages are generalisations of the copy language, which is a standard textbook example of a context-sensitive and noncontext- free language. In this work, we investigate a counter-intuitive phenomenon: with respect to alphabets of size 2 and 3, pattern languages can be regular or context-free in an unexpected way. For this regularity and context-freeness of pattern languages, we give several sufficient and necessary conditions and improve known results

On multi-head automata with restricted nondeterminism

In this work, we consider deterministic two-way multi-headautomata, the input heads of which are nondeterministically initialised, i.e., in every computation each input head is initially located at some nondeterministically chosen position of the input word. This model serves as an instrument to investigate restrictednondeterminism of two-way multi-headautomata. Our result is that, in terms of expressive power, two-way multi-headautomata with nondeterminism in form of nondeterministically initialising the input heads or with restrictednondeterminism in the classical way, i.e., in every accepting computation the number of nondeterministic steps is bounded by a constant, do not yield an advantage over their completely deterministic counter-parts with the same number of input heads. We conclude this paper with a brief application of this result

Automata with modulo counters and nondeterministic counter bounds

We introduce and investigate Nondeterministically Bounded Modulo Counter Automata (NBMCA), which are two-way one-head automata that comprise a constant number of modulo counters, where the counter bounds are nondeterministically guessed, and this is the only element of nondeterminism. NBMCA are tailored to recognising those languages that are characterised by the existence of a specific factorisation of their words, e. g., pattern languages. In this work, we subject NBMCA to a theoretically sound analysis

Patterns with bounded treewidth

We show that any parameter of patterns that is an upper bound for the treewidth of appropriate encodings of patterns as relational structures, if restricted to a constant, allows the membership problem for pattern languages to be solved in polynomial time. Furthermore, we identify a new such parameter, called the scope coincidence degree

A polynomial time match test for large classes of extended regular expressions

In the present paper, we study the match test for extended regular expressions. We approach this NP-complete problem by introducing a novel variant of two-way multihead automata, which reveals that the complexity of the match test is determined by a hidden combinatorial property of extended regular expressions, and it shows that a restriction of the corresponding parameter leads to rich classes with a polynomial time match test. For presentational reasons, we use the concept of pattern languages in order to specify extended regular expressions. While this decision, formally, slightly narrows the scope of our results, an extension of our concepts and results to more general notions of extended regular expressions is straightforward

Patterns with bounded treewidth

A pattern is a string consisting of variables and terminal symbols, and its language is the set of all words that can be obtained by substituting arbitrary words for the variables. The membership problem for pattern languages, i.e., deciding on whether or not a given word is in the pattern language of a given pattern is NP-complete. We show that any parameter of patterns that is an upper bound for the treewidth of appropriate encodings of patterns as relational structures, if restricted, allows the membership problem for pattern languages to be solved in polynomial time. Furthermore, we identify new such parameters

Automata with Modulo Counters and Nondeterministic Counter Bounds

We introduce and investigate Nondeterministically Bounded Modulo Counter Automata (NBMCA), which are two-way multi-head automata that comprise a constant number of modulo counters, where the counter bounds are nondeterministically guessed, and this is the only element of nondeterminism. NBMCA are tailored to recognising those languages that are characterised by the existence of a specific factorisation of their words, e. g., pattern languages. In this work, we subject NBMCA to a theoretically sound analysis