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### A Linear-Time Nominal μ-Calculus with Name Allocation

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### Abstract

Logics and automata models for languages over infinite alphabets, such as Freeze LTL and register automata, serve the verification of processes or documents with data. They relate tightly to formalisms over nominal sets, such as nondetermininistic orbit-finite automata (NOFAs), where names play the role of data. Reasoning problems in such formalisms tend to be computationally hard. Name-binding nominal automata models such as {regular nondeterministic nominal automata (RNNAs)} have been shown to be computationally more tractable. In the present paper, we introduce a linear-time fixpoint logic Bar-μTL} for finite words over an infinite alphabet, which features full negation and freeze quantification via name binding. We show by a nontrivial reduction to extended regular nondeterministic nominal automata that even though Bar-μTL} allows unrestricted nondeterminism and unboundedly many registers, model checking Bar-μTL} over RNNAs and satisfiability checking both have elementary complexity. For example, model checking is in 2ExpSpace, more precisely in parametrized ExpSpace, effectively with the number of registers as the parameter.

### BibTeX - Entry

@InProceedings{hausmann_et_al:LIPIcs.MFCS.2021.58,
author =	{Hausmann, Daniel and Milius, Stefan and Schr\"{o}der, Lutz},
title =	{{A Linear-Time Nominal \mu-Calculus with Name Allocation}},
booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
pages =	{58:1--58:18},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-201-3},
ISSN =	{1868-8969},
year =	{2021},
volume =	{202},
editor =	{Bonchi, Filippo and Puglisi, Simon J.},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
}