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A Linear-Time Nominal μ-Calculus with Name Allocation

Authors Daniel Hausmann , Stefan Milius , Lutz Schröder

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Author Details

Daniel Hausmann
  • Gothenburg University, Göteborg, Sweden
Stefan Milius
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Lutz Schröder
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

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Daniel Hausmann, Stefan Milius, and Lutz Schröder. A Linear-Time Nominal μ-Calculus with Name Allocation. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 58:1-58:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Verification by model checking
  • Model checking
  • linear-time logic
  • nominal sets


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