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Past, Present, and Infinite Future

Author Thomas Wilke

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Thomas Wilke

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Thomas Wilke. Past, Present, and Infinite Future. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 95:1-95:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ICALP.2016.95

Abstract

I was supposed to deliver one of the speeches at Wolfgang Thomas's retirement ceremony. Wolfgang had called me on the phone earlier and posed some questions about temporal logic, but I hadn't had good answers at the time. What I decided to do at the ceremony was to take up the conversation again and show how it could have evolved if only I had put more effort into answering his questions. Here is the imaginary conversation with Wolfgang. The contributions are (1) the first direct translation from counter-free omega-automata into future temporal formulas, (2) a definition of bimachines for omega-words, (3) a translation from arbitrary temporal formulas (including both, future and past operators) into counter-free omega-bimachines, and (4) an automata-based proof of separation: every arbitrary temporal formula is equivalent to a boolean combination of pure future, present, and pure past formulas when interpreted in omega-words.
Keywords
  • linear-time temporal logic
  • separation
  • backward deterministic omega-automata
  • counter freeness

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