21,135 research outputs found
The Wadge Hierarchy of Deterministic Tree Languages
We provide a complete description of the Wadge hierarchy for
deterministically recognisable sets of infinite trees. In particular we give an
elementary procedure to decide if one deterministic tree language is
continuously reducible to another. This extends Wagner's results on the
hierarchy of omega-regular languages of words to the case of trees.Comment: 44 pages, 8 figures; extended abstract presented at ICALP 2006,
Venice, Italy; full version appears in LMCS special issu
Advances and applications of automata on words and trees : abstracts collection
From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available
Edit Distance for Pushdown Automata
The edit distance between two words is the minimal number of word
operations (letter insertions, deletions, and substitutions) necessary to
transform to . The edit distance generalizes to languages
, where the edit distance from to
is the minimal number such that for every word from
there exists a word in with edit distance at
most . We study the edit distance computation problem between pushdown
automata and their subclasses. The problem of computing edit distance to a
pushdown automaton is undecidable, and in practice, the interesting question is
to compute the edit distance from a pushdown automaton (the implementation, a
standard model for programs with recursion) to a regular language (the
specification). In this work, we present a complete picture of decidability and
complexity for the following problems: (1)~deciding whether, for a given
threshold , the edit distance from a pushdown automaton to a finite
automaton is at most , and (2)~deciding whether the edit distance from a
pushdown automaton to a finite automaton is finite.Comment: An extended version of a paper accepted to ICALP 2015 with the same
title. The paper has been accepted to the LMCS journa
Deciding the Borel complexity of regular tree languages
We show that it is decidable whether a given a regular tree language belongs
to the class of the Borel hierarchy, or equivalently whether
the Wadge degree of a regular tree language is countable.Comment: 15 pages, 2 figure
Infinite games with finite knowledge gaps
Infinite games where several players seek to coordinate under imperfect
information are deemed to be undecidable, unless the information is
hierarchically ordered among the players.
We identify a class of games for which joint winning strategies can be
constructed effectively without restricting the direction of information flow.
Instead, our condition requires that the players attain common knowledge about
the actual state of the game over and over again along every play.
We show that it is decidable whether a given game satisfies the condition,
and prove tight complexity bounds for the strategy synthesis problem under
-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio
Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages
For a class L of languages let PDL[L] be an extension of Propositional
Dynamic Logic which allows programs to be in a language of L rather than just
to be regular. If L contains a non-regular language, PDL[L] can express
non-regular properties, in contrast to pure PDL.
For regular, visibly pushdown and deterministic context-free languages, the
separation of the respective PDLs can be proven by automata-theoretic
techniques. However, these techniques introduce non-determinism on the automata
side. As non-determinism is also the difference between DCFL and CFL, these
techniques seem to be inappropriate to separate PDL[DCFL] from PDL[CFL].
Nevertheless, this separation is shown but for programs without test operators.Comment: In Proceedings GandALF 2011, arXiv:1106.081
Polishness of some topologies related to word or tree automata
We prove that the B\"uchi topology and the automatic topology are Polish. We
also show that this cannot be fully extended to the case of a space of infinite
labelled binary trees; in particular the B\"uchi and the Muller topologies are
not Polish in this case.Comment: This paper is an extended version of a paper which appeared in the
proceedings of the 26th EACSL Annual Conference on Computer Science and
Logic, CSL 2017. The main addition with regard to the conference paper
consists in the study of the B\"uchi topology and of the Muller topology in
the case of a space of trees, which now forms Section
An Upper Bound on the Complexity of Recognizable Tree Languages
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular
tree language of infinite trees is in a class
for some natural number , where is the game quantifier. We
first give a detailed exposition of this result. Next, using an embedding of
the Wadge hierarchy of non self-dual Borel subsets of the Cantor space
into the class , and the notions of Wadge degree
and Veblen function, we argue that this upper bound on the topological
complexity of regular tree languages is much better than the usual
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Which Classes of Origin Graphs Are Generated by Transducers.
We study various models of transducers equipped with origin information. We consider the semantics of these models as particular graphs, called origin graphs, and we characterise the families of such graphs recognised by streaming string transducers
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