PP-2004-21: Automata and Fixed Point Logic: a Coalgebraic Perspective

PP-2004-21: Venema, Yde (2004) Automata and Fixed Point Logic: a Coalgebraic Perspective. [Report]

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This paper generalizes existing connections between automata and logic
to a coalgebraic level.
Let F be a standard endofunctor on Set that preserves weak pullbacks.
We introduce various notions of F-automata, devices that operate on
pointed F-coalgebras. The criterion under which such an automaton
accepts or rejects a pointed coalgebra is formulated in terms of an
infinite two-player graph game. We also introduce a language of
coalgebraic fixed point logic for F-coalgebras, and we provide a game
semantics for this language. Finally we show that any formula P of
the language can be transformed into an F-automaton A(P) which is
equivalent to P in the sense that A(P) accepts precisely those pointed
F-coalgebras in which P holds.

Item Type: Report
Report Nr: PP-2004-21
Series Name: Prepublication (PP) Series
Year: 2004
Uncontrolled Keywords: coalgebra; automata; modal logic; fixed point operators; game semantics; bisimulation; parity games
Subjects: Logic
Depositing User: Yde Venema
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/132

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