Constraint LTL with Remote Access

Authors Ashwin Bhaskar , M. Praveen

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Author Details

Ashwin Bhaskar
  • Chennai Mathematical Institute, India
M. Praveen
  • Chennai Mathematical Institute, India
  • CNRS IRL ReLaX, Chennai, India

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Ashwin Bhaskar and M. Praveen. Constraint LTL with Remote Access. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 41:1-41:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Constraint Linear Temporal Logic (CLTL) is an extension of LTL that is interpreted on sequences of valuations of variables over an infinite domain. The atomic formulas are interpreted as constraints on the valuations. The atomic formulas can constrain valuations at the current position and positions that are a fixed distance apart (e.g., the previous position or the second previous position and so on). The satisfiability problem for CLTL is known to be Pspace-complete. We generalize CLTL to let atomic formulas access positions that are unboundedly far away in the past. We annotate the sequence of valuations with letters from a finite alphabet and use regular expressions on the finite alphabet to control how atomic formulas access past positions. We prove that the satisfiability problem for this extension of the logic is decidable in cases where the domain is dense and open with respect to a linear order (e.g., rational numbers with the usual linear order). We prove that it is also decidable over integers with linear order and equality.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Verification by model checking
  • Theory of computation → Automata over infinite objects
  • Constraint LTL
  • Regular Expressions
  • MSO formulas
  • Satisfiability
  • Büchi automata


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