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Explorability in Pushdown Automata

Authors Ayaan Bedi , Karoliina Lehtinen

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Subject Classification

ACM Subject Classification
  • Theory of computation → Automata extensions
Keywords
  • Pushdown automata
  • nondeterminism
  • explorability
  • history-determinism

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Abstract

We study explorability, a measure of nondeterminism in pushdown automata, which generalises history-determinism. An automaton is k-explorable if, while reading the input, it suffices to follow k concurrent runs, built step-by-step based only on the input seen so far, to construct an accepting one, if it exists. We show that the class of explorable PDAs lies strictly between history-deterministic and fully nondeterministic PDAs in terms of both expressiveness and succinctness. In fact increasing explorability induces an infinite hierarchy: each level k defines a strictly more expressive class than level k-1, yet the entire class remains less expressive than general nondeterministic PDAs. We then introduce a parameterized notion of explorability, where the number of runs may depend on input length, and show that exponential explorability precisely captures the context-free languages. Finally, we prove that explorable PDAs can be doubly exponentially more succinct than history-deterministic ones, and that the succinctness gap between deterministic and 2-explorable PDAs is not recursively enumerable. These results position explorability as a robust and operationally meaningful measure of nondeterminism for pushdown systems.

Cite As Get BibTex

Ayaan Bedi and Karoliina Lehtinen. Explorability in Pushdown Automata. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FSTTCS.2025.12

Author Details

Ayaan Bedi
  • Chennai Mathematical Institute, India
Karoliina Lehtinen
  • CNRS Researcher, Aix-Marseille Université, LIS, France

Funding

This work is in part funded by ANR Project QuaSy ANR-23-CE48-0008 and part supported by ReLaX, Research Lab in Computer Science, CNRS IRL 2000.

Acknowledgements

We are grateful to Aditya Prakash for his insightful input and helpful discussions.

References

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