Model checking linear properties of prefix-recognizable systems

Orna Kupferman; Nir Piterman; Moshe Y. Vardi

doi:10.1007/3-540-45657-0_31

Model checking linear properties of prefix-recognizable systems

Orna Kupferman, Nir Piterman, Moshe Y. Vardi

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

17 Scopus citations

Abstract

We develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by an alternating two-way automaton that navigates through the tree. We introduce path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. In particular, two-way nondeterministic path automata enable exactly the type of navigation that is required in order to check linear properties of infinite-state sequential systems. We demonstrate the versatility of the automata-theoretic approach by solving several versions of the model-checking problem for LTL specifications and prefix-recognizable systems. Our algorithm is exponential in both the size of (the description of) the system and the size of the LTL specification, and we prove a matching lower bound. This is the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems. Our framework also handles systems with regular labeling.

Original language	English
Title of host publication	Computer Aided Verification - 14th International Conference, CAV 2002, Proceedings
Editors	Ed Brinksma, Kim Guldstrand Larsen
Publisher	Springer Verlag
Pages	371-385
Number of pages	15
ISBN (Electronic)	9783540439974
DOIs	https://doi.org/10.1007/3-540-45657-0_31
State	Published - 2002
Event	14th International Conference on Computer Aided Verification, CAV 2002 - Copenhagen, Denmark Duration: 27 Jul 2002 → 31 Jul 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2404
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th International Conference on Computer Aided Verification, CAV 2002
Country/Territory	Denmark
City	Copenhagen
Period	27/07/02 → 31/07/02

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

Access to Document

10.1007/3-540-45657-0_31

Cite this

Kupferman, O., Piterman, N., & Vardi, M. Y. (2002). Model checking linear properties of prefix-recognizable systems. In E. Brinksma, & K. G. Larsen (Eds.), Computer Aided Verification - 14th International Conference, CAV 2002, Proceedings (pp. 371-385). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2404). Springer Verlag. https://doi.org/10.1007/3-540-45657-0_31

Kupferman, Orna ; Piterman, Nir ; Vardi, Moshe Y. / Model checking linear properties of prefix-recognizable systems. Computer Aided Verification - 14th International Conference, CAV 2002, Proceedings. editor / Ed Brinksma ; Kim Guldstrand Larsen. Springer Verlag, 2002. pp. 371-385 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{3a944bb456424b3191822e79b627633c,

title = "Model checking linear properties of prefix-recognizable systems",

abstract = "We develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by an alternating two-way automaton that navigates through the tree. We introduce path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. In particular, two-way nondeterministic path automata enable exactly the type of navigation that is required in order to check linear properties of infinite-state sequential systems. We demonstrate the versatility of the automata-theoretic approach by solving several versions of the model-checking problem for LTL specifications and prefix-recognizable systems. Our algorithm is exponential in both the size of (the description of) the system and the size of the LTL specification, and we prove a matching lower bound. This is the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems. Our framework also handles systems with regular labeling.",

author = "Orna Kupferman and Nir Piterman and Vardi, {Moshe Y.}",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2002.; 14th International Conference on Computer Aided Verification, CAV 2002 ; Conference date: 27-07-2002 Through 31-07-2002",

year = "2002",

doi = "10.1007/3-540-45657-0_31",

language = "אנגלית",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "371--385",

editor = "Ed Brinksma and Larsen, {Kim Guldstrand}",

booktitle = "Computer Aided Verification - 14th International Conference, CAV 2002, Proceedings",

address = "גרמניה",

}

Kupferman, O, Piterman, N & Vardi, MY 2002, Model checking linear properties of prefix-recognizable systems. in E Brinksma & KG Larsen (eds), Computer Aided Verification - 14th International Conference, CAV 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2404, Springer Verlag, pp. 371-385, 14th International Conference on Computer Aided Verification, CAV 2002, Copenhagen, Denmark, 27/07/02. https://doi.org/10.1007/3-540-45657-0_31

Model checking linear properties of prefix-recognizable systems. / Kupferman, Orna; Piterman, Nir; Vardi, Moshe Y.
Computer Aided Verification - 14th International Conference, CAV 2002, Proceedings. ed. / Ed Brinksma; Kim Guldstrand Larsen. Springer Verlag, 2002. p. 371-385 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2404).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Model checking linear properties of prefix-recognizable systems

AU - Kupferman, Orna

AU - Piterman, Nir

AU - Vardi, Moshe Y.

PY - 2002

Y1 - 2002

N2 - We develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by an alternating two-way automaton that navigates through the tree. We introduce path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. In particular, two-way nondeterministic path automata enable exactly the type of navigation that is required in order to check linear properties of infinite-state sequential systems. We demonstrate the versatility of the automata-theoretic approach by solving several versions of the model-checking problem for LTL specifications and prefix-recognizable systems. Our algorithm is exponential in both the size of (the description of) the system and the size of the LTL specification, and we prove a matching lower bound. This is the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems. Our framework also handles systems with regular labeling.

AB - We develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by an alternating two-way automaton that navigates through the tree. We introduce path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. In particular, two-way nondeterministic path automata enable exactly the type of navigation that is required in order to check linear properties of infinite-state sequential systems. We demonstrate the versatility of the automata-theoretic approach by solving several versions of the model-checking problem for LTL specifications and prefix-recognizable systems. Our algorithm is exponential in both the size of (the description of) the system and the size of the LTL specification, and we prove a matching lower bound. This is the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems. Our framework also handles systems with regular labeling.

UR - http://www.scopus.com/inward/record.url?scp=84937555009&partnerID=8YFLogxK

U2 - 10.1007/3-540-45657-0_31

DO - 10.1007/3-540-45657-0_31

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84937555009

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 371

EP - 385

BT - Computer Aided Verification - 14th International Conference, CAV 2002, Proceedings

A2 - Brinksma, Ed

A2 - Larsen, Kim Guldstrand

PB - Springer Verlag

T2 - 14th International Conference on Computer Aided Verification, CAV 2002

Y2 - 27 July 2002 through 31 July 2002

ER -

Kupferman O, Piterman N, Vardi MY. Model checking linear properties of prefix-recognizable systems. In Brinksma E, Larsen KG, editors, Computer Aided Verification - 14th International Conference, CAV 2002, Proceedings. Springer Verlag. 2002. p. 371-385. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45657-0_31

Model checking linear properties of prefix-recognizable systems

Abstract

Publication series

Conference

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this