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A Finite Semantics of SimplyTyped Lambda Terms for Infinite Runs of Automata

Summary: A Finite Semantics of Simply­Typed Lambda Terms
for Infinite Runs of Automata
Klaus Aehlig
Mathematisches Institut
Ludwig­Maximilians­Universit˜at M˜unchen
Theresienstr. 39, 80333 M˜unchen, Germany
Abstract. Model checking properties are often described by means of finite au­
tomata. Any particular such automaton divides the set of infinite trees into finitely
many classes, according to which state has an infinite run. Building the full type
hierarchy upon this interpretation of the base type gives a finite semantics for
simply­typed lambda­trees.
A calculus based on this semantics is proven sound and complete. In particular,
for regular infinite lambda­trees it is decidable whether a given automaton has a
run or not. As regular lambda­trees are precisely recursion schemes, this decid­
ability result holds for arbitrary recursion schemes of arbitrary level, without any
syntactical restriction. This partially solves an open problem of Knapik, Niwinski
and Urzyczyn.
1 Introduction and Related Work
The lambda calculus has long been used as a model of computation. Restricting it to


Source: Aehlig, Klaus T. - Institut für Informatik, Ludwig-Maximilians-Universität München


Collections: Mathematics; Computer Technologies and Information Sciences