The Tree Width of Separation Logic with Recursive Definitions

ROGALEWICZ, A.; ŠIMÁČEK, J.; IOSIF, R.

Original Title

The Tree Width of Separation Logic with Recursive Definitions

English Title

The Tree Width of Separation Logic with Recursive Definitions

Type

Report

Original Abstract

Separation Logic is a widely used formalism for describing dynamically
allocated linked data structures, such as lists, trees, etc. The decidability
status of various fragments of the logic constitutes a long standing open problem. Current results report on techniques to decide satisfiability and validity of entailments for Separation Logic(s) over lists (possibly with data). In this paper we establish a more general decidability result. We prove that any Separation Logic formula using rather general recursively defined predicates is decidable for satisfiability, and moreover, entailments between such formulae are decidable for validity. These predicates are general enough to define (doubly-) linked lists, trees, and structures more general than trees, such as trees whose leaves are chained in a list. The decidability proofs are by reduction to decidability ofMonadic Second Order Logic on graphs with bounded tree width.

English abstract

Separation Logic is a widely used formalism for describing dynamically
allocated linked data structures, such as lists, trees, etc. The decidability
status of various fragments of the logic constitutes a long standing open problem. Current results report on techniques to decide satisfiability and validity of entailments for Separation Logic(s) over lists (possibly with data). In this paper we establish a more general decidability result. We prove that any Separation Logic formula using rather general recursively defined predicates is decidable for satisfiability, and moreover, entailments between such formulae are decidable for validity. These predicates are general enough to define (doubly-) linked lists, trees, and structures more general than trees, such as trees whose leaves are chained in a list. The decidability proofs are by reduction to decidability ofMonadic Second Order Logic on graphs with bounded tree width.

Authors

ROGALEWICZ, A.; ŠIMÁČEK, J.; IOSIF, R.

Released

04.04.2013

Location

arXiv:1301.5139

Pages count

31

URL

http://arxiv.org/abs/1301.5139

Full text in the Digital Library

http://hdl.handle.net/

BibTex

@misc{BUT192895,
  author="Adam {Rogalewicz} and Jiří {Šimáček} and Iosif {Radu}",
  title="The Tree Width of Separation Logic with Recursive Definitions",
  year="2013",
  pages="31",
  address="arXiv:1301.5139",
  url="http://arxiv.org/abs/1301.5139"
}