DSpace Collection:
https://dspace.lboro.ac.uk/2134/2396
20180309T10:14:46Z

The word problem for omegaterms over the TrotterWeil hierarchy
https://dspace.lboro.ac.uk/2134/31950
Title: The word problem for omegaterms over the TrotterWeil hierarchy
Authors: Kufleitner, Manfred; Wachter, Jan Philipp
Abstract: © 2017 Springer Science+Business Media New York For two given ωterms α and β, the word problem for ωterms over a variety V asks whether α = β in all monoids in V. We show that the word problem for ωterms over each level of the TrotterWeil Hierarchy is decidable. More precisely, for every fixed variety in the TrotterWeil Hierarchy, our approach yields an algorithm in nondeterministic logarithmic space (NL). In addition, we provide deterministic polynomial time algorithms which are more efficient than straightforward translations of the NLalgorithms. As an application of our results, we show that separability by the socalled corners of the TrotterWeil Hierarchy is witnessed by ωterms (this property is also known as ωreducibility). In particular, the separation problem for the corners of the TrotterWeil Hierarchy is decidable.
Description: This paper is in closed access until 16th May 2018.
20170101T00:00:00Z

Green’s relations in finite transformation semigroups
https://dspace.lboro.ac.uk/2134/31949
Title: Green’s relations in finite transformation semigroups
Authors: Fleischer, Lukas; Kufleitner, Manfred
Abstract: © Springer International Publishing AG 2017. We consider the complexity of Green’s relations when the semigroup is given by transformations on a finite set. Green’s relations can be defined by reachability in the (right/left/twosided) Cayley graph. The equivalence classes then correspond to the strongly connected components. It is not difficult to show that, in the worst case, the number of equivalence classes is in the same order of magnitude as the number of elements. Another important parameter is the maximal length of a chain of components. Our main contribution is an exponential lower bound for this parameter. There is a simple construction for an arbitrary set of generators. However, the proof for constant alphabet is rather involved. Our results also apply to automata and their syntactic semigroups.
Description: This is a precopyedited version of a contribution published in Computer Science – Theory and Applications: The 12th International Computer Science Symposium in Russia (CSR 2017) edited by Weil, P. published by Springer International. The definitive authenticated version is available online via https://doi.org/10.1007/9783319587479_12 . It is in closed access until 6th May 2018.
20170101T00:00:00Z

Level Two of the quantifier alternation hierarchy over infinite words
https://dspace.lboro.ac.uk/2134/31947
Title: Level Two of the quantifier alternation hierarchy over infinite words
Authors: Kufleitner, Manfred; Walter, Tobias
Abstract: © 2017 Springer Science+Business Media, LLC The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of firstorder logic over infinite words; the membership problem asks for a given language whether it is definable in some fixed fragment. The alphabetic topology was introduced as part of an effective characterization of the fragment Σ 2 over infinite words. Here, Σ 2 consists of the firstorder formulas with two blocks of quantifiers, starting with an existential quantifier. Its Boolean closure is (Formula presented.). Our first main result is an effective characterization of the Boolean closure of the alphabetic topology, that is, given an ωregular language L, it is decidable whether L is a Boolean combination of open sets in the alphabetic topology. This is then used for transferring Place and Zeitoun’s recent decidability result for (Formula presented.) from finite to infinite words.
Description: This journal article is part of the following topical collections: Computer Science Symposium in Russia, it is in closed access until 4th Aug 2018.
20170101T00:00:00Z

Green’s relations in deterministic finite automata
https://dspace.lboro.ac.uk/2134/31946
Title: Green’s relations in deterministic finite automata
Authors: Fleischer, Lukas; Kufleitner, Manfred
Abstract: Green’s relations are a fundamental tool in the structure theory of semigroups. They can be defined by reachability in the (right/left/twosided) Cayley graph. The equivalence classes of Green’s relations then correspond to the strongly connected components. We study the complexity of Green’s relations in semigroups generated by transformations on a
finite set. We show that, in the worst case, the number of equivalence classes is in the same order of magnitude as the number of elements.
Another important parameter is the maximal length of a chain of strongly connected components. Our main contribution is an exponential lower bound for this parameter. There is a simple construction for an arbitrary
set of generators. However, the proof for a constant size alphabet is rather involved. We also investigate the special cases of unary and binary alphabets. All these results are extended to deterministic finite automata and their syntactic semigroups.
Description: This journal article is part of the following topical collections: Computer Science Symposium in Russia, it is in closed access until 12th Feb 2019.
20180101T00:00:00Z