Furthermore, by Proposition 6.19, ? admits a non?-controlled FO-model such that the interpretation of p is finite, since ?y 1 , . . . , y m . ? 1 has a non-?-controlled SL-model. By Lemma 6.18, and by definition of ?, this entails that there exists an FO-model of ? with strictly more than N (? ) unallocated elements and such that the interpretation of p is finite. By Lemma 5.29 (2), the formula ? (hence also ? 1 ) contains no positive occurrence of a formula of the form |h| ? |U | ? i, and by definition, ? 1 contains no positive occurrence of a formula alloc(x ), N (? 2 ) ? N (? ) and ? |= ?y 1 , . . . , y m . ? 1 , thus ?y 1 , . . . , y m . ? 1 has a non-?-controlled model. By Proposition 4.10, the formula ? = ? (?y 1 , . . . , y m . ? 1 ) ? A(?y 1, vol.4, p.2072, 2071. ,
Foundations for Decision Problems in Separation Logic with General Inductive Predicates, Foundations of Software Science and Computation Structures, Anca Muscholl, pp.411-425, 2014. ,
, Computational Complexity -A Modern Approach, 2009.
The Classical Decision Problem, 1997. ,
Automated Cyclic Entailment Proofs in Separation Logic, Automated Deduction -CADE-23: 23rd International Conference on Automated Deduction, pp.131-146, 2011. ,
A Decision Procedure for Satisfiability in Separation Logic with Inductive Predicates, Proceedings 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) (CSL-LICS '14), vol.25, pp.1-25, 2014. ,
From Separation Logic to First-Order Logic, Foundations of Software Science and Computational Structures, pp.395-409, 2005. ,
Computability and Complexity Results for a Spatial Assertion Language for Data Structures, FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science, pp.108-119, 2001. ,
Expressive Completeness of Separation Logic with Two Variables and No Separating Conjunction, ACM Trans. Comput. Log, vol.17, 2016. ,
The Effects of Adding Reachability Predicates in Propositional Separation Logic, Foundations of Software Science and Computation Structures -21st International Conference, FOSSACS 2018, Held as Part of the European Joint Conferences on Theory and Practice of Software, vol.10803, pp.476-493, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-02366664
Prenex Separation Logic with One Selector Field, Automated Reasoning with Analytic Tableaux and Related Methods -28th International Conference, vol.11714, pp.409-427, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02323468
The Bernays-Schönfinkel-Ramsey Class of Separation Logic on Arbitrary Domains, Foundations of Software Science and Computation Structures -22nd International Conference, FOSSACS 2019, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019, vol.11425, pp.242-259, 2019. ,
Combinatorial Theorems on Classifications of Subsets of a Given Set, Proceedings of the London Mathematical Society, pp.417-439, 1952. ,
Combinations of Theories and the Bernays-Schönfinkel-Ramsey Class, Proceedings of 4th International Verification Workshop in connection with CADE-21, vol.259, 2007. ,
The Tree Width of Separation Logic with Recursive Definitions, Proc. of CADE-24, vol.7898, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01418897
BI as an assertion language for mutable data structures, ACM SIGPLAN Notices, vol.36, pp.14-26, 2001. ,
Effective Entailment Checking for Separation Logic with Inductive Definitions, Tools and Algorithms for the Construction and Analysis of Systems -25th International Conference, TACAS 2019, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019, vol.11428, pp.319-336, 2019. ,
A Decidable Fragment in Separation Logic with Inductive Predicates and Arithmetic, Computer Aided Verification -29th International Conference, vol.10427, pp.495-517, 2017. ,
Complexity results for classes of quantificational formulas, J. Comput. System Sci, vol.21, pp.317-353, 1980. ,
Separation Logic preserves the Expressive Power of Classical Logic, SPACE, 2004. ,
Local Reasoning about Programs that Alter Data Structures, Computer Science Logic, 15th International Workshop, CSL 2001. 10th Annual Conference of the EACSL, pp.1-19, 2001. ,
Computational Complexity, 1994. ,
On a Problem of Formal Logic, Classic Papers in Combinatorics, pp.1-24, 1987. ,
Reasoning in the Bernays-Schönfinkel-Ramsey Fragment of Separation Logic, Verification, Model Checking, and Abstract Interpretation, pp.462-482, 2017. ,
Separation Logic: A Logic for Shared Mutable Data Structures, Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science (LICS '02), pp.55-74, 2002. ,
Relationships between nondeterministic and deterministic tape complexities, J. Comput. System Sci, vol.4, pp.177-192, 1970. ,
The Complexity of Relational Query Languages, Proceedings of the 14th Annual ACM Symposium on Theory of Computing, pp.137-146, 1982. ,