Determinacy of Infinite Games: Perspectives of the Algorithmic Approach (Invited Talk)

Author Wolfgang Thomas



PDF
Thumbnail PDF

File

LIPIcs.CSL.2017.6.pdf
  • Filesize: 202 kB
  • 1 pages

Document Identifiers

Author Details

Wolfgang Thomas

Cite As Get BibTex

Wolfgang Thomas. Determinacy of Infinite Games: Perspectives of the Algorithmic Approach (Invited Talk). In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, p. 6:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.CSL.2017.6

Abstract

Determinacy of infinite two-player games is a topic of descriptive set theory that has triggered intensive research in theoretical computer science since 1957 when A. Church formulated his "synthesis problem" (regarding the construction of  circuits with infinite behavior from logical specifications). In the first part of the lecture we review the fascinating development of the algorithmic theory of infinite games that was started by Church's problem, that enriched automata theory and related fields, and that led to interesting applications in verification and program synthesis. In the second part we turn to the question how to lift this theory from the case of the Cantor space (where a play is a sequence of bits) to the case of the Baire space (where a play is a sequence of natural numbers). While this step does not involve difficulties in classical descriptive set theory, the algorithmic approach raises non-trivial questions since it requires to consider automata that work over infinite alphabets. We  present recent results (joint work with B. Brütsch) that provide a solution of Church's synthesis problem in this context, and we point to numerous questions that are still open.

Subject Classification

Keywords
  • Infinite games
  • descriptive set theory
  • automata theory
  • transducers
  • automatic synthesis

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail