arXiv subjects

Markus L. Schmid

Publications and source records attributed to Markus L. Schmid.

23 records · Page 2Linked to original sources

arXiv2018

Deterministic Regular Expressions With Back-References

Most modern libraries for regular expression matching allow back-references (i.e., repetition operators) that substantially increase expressive power, but also lead to intractability. In order to find a better balance between expressiveness and tractability, we combine these with the notion of determinism for regular expressions used in XML DTDs and XML Schema. This includes the definition of a suitable automaton model, and a generalization of the Glushkov construction. We demonstrate that, compared to their non-deterministic superclass, these deterministic regular expressions with back-references have desirable algorithmic properties (i.e., efficiently solvable membership problem and some decidable problems in static analysis), while, at the same time, their expressive power exceeds that of deterministic regular expressions without back-references.

cs.FL↗

arXiv2017

Combinatorial Properties and Recognition of Unit Square Visibility Graphs

Unit square (grid) visibility graphs (USV and USGV, resp.) are described by axis-parallel visibility between unit squares placed (on integer grid coordinates) in the plane. We investigate combinatorial properties of these graph classes and the hardness of variants of the recognition problem, i.e., the problem of representing USGV with fixed visibilities within small area and, for USV, the general recognition problem.

cs.CG↗

arXiv2017

Two-Dimensional Pattern Languages

We introduce several classes of array languages obtained by generalising Angluin's pattern languages to the two-dimensional case. These classes of two-dimensional pattern languages are compared with respect to their expressive power and their closure properties are investigated.

cs.FL↗

arXiv2017

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.

cs.FL↗

arXiv2015

Characterization and Complexity Results on Jumping Finite Automata

In a jumping finite automaton, the input head can jump to an arbitrary position within the remaining input after reading and consuming a symbol. We characterize the corresponding class of languages in terms of special shuffle expressions and survey other equivalent notions from the existing literature. Moreover, we present several results concerning computational hardness and algorithms for parsing and other basic tasks concerning jumping finite automata.

cs.FL↗