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Computing the Width of Non-deterministic Automata

Denis Kuperberg ; Anirban Majumdar.

We introduce a measure called width, quantifying the amount of nondeterminism in automata. Width generalises the notion of good-for-games (GFG) automata, that correspond to NFAs of width 1, and where an accepting run can be built on-the-fly on any accepted input. We describe an incremental&nbsp;[&hellip;]

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Positive First-order Logic on Words and Graphs

Denis Kuperberg.

We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This provides a simple proof that Lyndon's preservation theorem fails on&nbsp;[&hellip;]

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