11 research outputs found
Formats of Winning Strategies for Six Types of Pushdown Games
The solution of parity games over pushdown graphs (Walukiewicz '96) was the
first step towards an effective theory of infinite-state games. It was shown
that winning strategies for pushdown games can be implemented again as pushdown
automata. We continue this study and investigate the connection between game
presentations and winning strategies in altogether six cases of game arenas,
among them realtime pushdown systems, visibly pushdown systems, and counter
systems. In four cases we show by a uniform proof method that we obtain
strategies implementable by the same type of pushdown machine as given in the
game arena. We prove that for the two remaining cases this correspondence
fails. In the conclusion we address the question of an abstract criterion that
explains the results
Relating Automata-theoretic Hierarchies to Complexity-theoretic Hierarchies
We show that some natural refinements of the Straubing and Brzozowski
hierarchies correspond (via the so called leaf-languages) step by step to
similar refinements of the polynomial-time hierarchy. This extends a result of
Burtschik and Vollmer on relationship between the Straubing and the
polynomial hierarchies. In particular, this applies to the Boolean hierarchy
and the plus-hierarchy
Towards a descriptive set theory for domain-like structures
AbstractThis is a survey of results in descriptive set theory for domains and similar spaces, with the emphasis on the ω-algebraic domains. We try to demonstrate that the subject is interesting in its own right and is closely related to some areas of theoretical computer science. Since the subject is still in its beginning, we discuss in detail several open questions and possible future development. We also mention some relevant facts of (effective) descriptive set theory
Hierarchies and reducibilities on regular languages related to modulo counting
We discuss some known and introduce some new hierarchies and
reducibilities on regular languages, with the emphasis on the
quantifier-alternation and difference hierarchies of the
quasi-aperiodic languages. The non-collapse of these hierarchies and
decidability of some levels are established. Complete sets in the
levels of the hierarchies under the polylogtime and some
quantifier-free reducibilities are found. Some facts about the
corresponding degree structures are established. As an application,
we characterize the regular languages whose balanced leaf-language
classes are contained in the polynomial hierarchy. For any
discussed reducibility we try to give motivations and open
questions, in a hope to convince the reader that the study of these
reducibilities is interesting for automata theory and computational
complexity
Classifying ω-Regular Partitions
Abstract. We try to develop a theory of ω-regular partitions in parallel with the theory around the Wagner hierarchy of regular ω-languages. In particular, we generalize a theorem of L. Staiger and K. Wagner to the case of partitions, prove decidability of all levels of the Boolean hierarchy of regular partitions over open sets, establish coincidence of reducibilities by continuous functions and by functions computed by finite automata on the class of regular ∆ 0 2-partitions, and show undecidability of the firstorder theory of the structure of Wadge degrees of regular k-partitions for all k ≥ 3