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Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.117
A Rice’s Theorem for Abstract Semantics

Authors: Paolo Baldan, Francesco Ranzato, and Linpeng Zhang

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
Classical results in computability theory, notably Rice’s theorem, focus on the extensional content of programs, namely, on the partial recursive functions that programs compute. Later and more recent work investigated intensional generalisations of such results that take into account the way in which functions are computed, thus affected by the specific programs computing them. In this paper, we single out a novel class of program semantics based on abstract domains of program properties that are able to capture nonextensional aspects of program computations, such as their asymptotic complexity or logical invariants, and allow us to generalise some foundational computability results such as Rice’s Theorem and Kleene’s Second Recursion Theorem to these semantics. In particular, it turns out that for this class of abstract program semantics, any nontrivial abstract property is undecidable and every decidable overapproximation necessarily includes an infinite set of false positives which covers all values of the semantic abstract domain.
Cite as

Paolo Baldan, Francesco Ranzato, and Linpeng Zhang. A Rice’s Theorem for Abstract Semantics. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 117:1-117:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{baldan_et_al:LIPIcs.ICALP.2021.117,
  author =	{Baldan, Paolo and Ranzato, Francesco and Zhang, Linpeng},
  title =	{{A Rice’s Theorem for Abstract Semantics}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{117:1--117:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.117},
  URN =		{urn:nbn:de:0030-drops-141860},
  doi =		{10.4230/LIPIcs.ICALP.2021.117},
  annote =	{Keywords: Computability Theory, Recursive Function, Rice’s Theorem, Kleene’s Second Recursion Theorem, Program Analysis, Affine Program Invariants}
}
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