Publication result detail

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

Paper in proceedings outside WoS and Scopus

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.

Keywords

Separation logic, Tree width, MSO, Graphs

Key words in English

Separation logic, Tree width, MSO, Graphs

Authors

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

RIV year

2014

Released

12.03.2013

Publisher

Springer Verlag

Location

Berlin

ISBN

978-3-642-38573-5

Book

Automated Deduction - CADE-24

Edition

Lecture Notes in Artificial Intelligence

ISBN

0302-9743

Periodical

Lecture Notes in Computer Science

Volume

2013

Number

7898

State

Federal Republic of Germany

Pages from

21

Pages to

38

Pages count

18

URL

http://link.springer.com/chapter/10.1007/978-3-642-38574-2_2

BibTex

@inproceedings{BUT103458,
  author="Adam {Rogalewicz} and Jiří {Šimáček} and Iosif {Radu}",
  title="The Tree Width of Separation Logic with Recursive Definitions",
  booktitle="Automated Deduction - CADE-24",
  year="2013",
  series="Lecture Notes in Artificial Intelligence",
  journal="Lecture Notes in Computer Science",
  volume="2013",
  number="7898",
  pages="21--38",
  publisher="Springer Verlag",
  address="Berlin",
  doi="10.1007/978-3-642-38574-2\{_}2",
  isbn="978-3-642-38573-5",
  issn="0302-9743",
  url="http://link.springer.com/chapter/10.1007/978-3-642-38574-2_2"
}