Article

Undecidability of Propositional Separation Logic and Its Neighbours

Authors:

James Brotherston,

Max KanovichAuthors Info & Claims

LICS '10: Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science

Pages 130 - 139

https://doi.org/10.1109/LICS.2010.24

Published: 11 July 2010 Publication History

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Abstract

Separation logic has proven an effective formalism for the analysis of memory-manipulating programs. We show that the purely propositional fragment of separation logic is undecidable. In fact, for *any* choice of concrete heap-like model of separation logic, validity in that model remains undecidable. Besides its intrinsic technical interest, this result also provides new insights into the nature of decidable fragments of separation logic. In addition, we show that a number of propositional systems which approximate separation logic are undecidable as well. In particular, these include both Boolean BI and Classical BI. All of our undecidability results are obtained by means of a single direct encoding of Minsky machines.

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Demri SGalmiche DLarchey-Wendling DMéry D(2017)Separation Logic with One Quantified VariableTheory of Computing Systems10.1007/s00224-016-9713-161:2(371-461)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1007/s00224-016-9713-1
Demri SDeters MHenzinger TMiller D(2014)Expressive completeness of separation logic with two variables and no separating conjunctionProceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1145/2603088.2603142(1-10)Online publication date: 14-Jul-2014
https://dl.acm.org/doi/10.1145/2603088.2603142
Lee WPark S(2014)A proof system for separation logic with magic wandACM SIGPLAN Notices10.1145/2578855.253587149:1(477-490)Online publication date: 8-Jan-2014
https://dl.acm.org/doi/10.1145/2578855.2535871
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LICS '10: Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science

July 2010

429 pages

ISBN:9780769541143

Publisher

IEEE Computer Society

United States

Publication History

Published: 11 July 2010

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Demri SGalmiche DLarchey-Wendling DMéry D(2017)Separation Logic with One Quantified VariableTheory of Computing Systems10.1007/s00224-016-9713-161:2(371-461)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1007/s00224-016-9713-1
Demri SDeters MHenzinger TMiller D(2014)Expressive completeness of separation logic with two variables and no separating conjunctionProceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1145/2603088.2603142(1-10)Online publication date: 14-Jul-2014
https://dl.acm.org/doi/10.1145/2603088.2603142
Lee WPark S(2014)A proof system for separation logic with magic wandACM SIGPLAN Notices10.1145/2578855.253587149:1(477-490)Online publication date: 8-Jan-2014
https://dl.acm.org/doi/10.1145/2578855.2535871
Hóu ZClouston RGoré RTiu A(2014)Proof search for propositional abstract separation logics via labelled sequentsACM SIGPLAN Notices10.1145/2578855.253586449:1(465-476)Online publication date: 8-Jan-2014
https://dl.acm.org/doi/10.1145/2578855.2535864
Brotherston JKanovich M(2014)Undecidability of Propositional Separation Logic and Its NeighboursJournal of the ACM10.1145/254266761:2(1-43)Online publication date: 24-Apr-2014
https://dl.acm.org/doi/10.1145/2542667
Lee WPark SJagannathan SSewell P(2014)A proof system for separation logic with magic wandProceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages10.1145/2535838.2535871(477-490)Online publication date: 11-Jan-2014
https://dl.acm.org/doi/10.1145/2535838.2535871
Hóu ZClouston RGoré RTiu AJagannathan SSewell P(2014)Proof search for propositional abstract separation logics via labelled sequentsProceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages10.1145/2535838.2535864(465-476)Online publication date: 11-Jan-2014
https://dl.acm.org/doi/10.1145/2535838.2535864
Park JSeo JPark S(2013)A theorem prover for Boolean BIACM SIGPLAN Notices10.1145/2480359.242909548:1(219-232)Online publication date: 23-Jan-2013
https://dl.acm.org/doi/10.1145/2480359.2429095
Park JSeo JPark SGiacobazzi RCousot R(2013)A theorem prover for Boolean BIProceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages10.1145/2429069.2429095(219-232)Online publication date: 23-Jan-2013
https://dl.acm.org/doi/10.1145/2429069.2429095
Larchey-Wendling DGalmiche D(2013)Nondeterministic Phase Semantics and the Undecidability of Boolean BIACM Transactions on Computational Logic10.1145/2422085.242209114:1(1-41)Online publication date: 1-Feb-2013
https://dl.acm.org/doi/10.1145/2422085.2422091
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