메뉴 건너뛰기




Volumn 313, Issue 1, 2004, Pages 17-29

Counting the solutions of Presburger equations without enumerating them

Author keywords

Automata; Counting; Presburger arithmetic; Symbolic representation systems

Indexed keywords

ALGORITHMS; DIGITAL ARITHMETIC; PROBLEM SOLVING; SET THEORY; VECTORS;

EID: 0742267112     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2003.10.002     Document Type: Conference Paper
Times cited : (17)

References (20)
  • 1
    • 84947916935 scopus 로고    scopus 로고
    • Diophantine equations, Presburger arithmetic and finite automata
    • Proc. CAAP'96, Springer, Berlin
    • A. Boudet, H. Comon, Diophantine equations, Presburger arithmetic and finite automata, in: Proc. CAAP'96, Lecture Notes in Computer Science, Vol. 1059, Springer, Berlin, 1996, pp. 30-43.
    • (1996) Lecture Notes in Computer Science , vol.1059 , pp. 30-43
    • Boudet, A.1    Comon, H.2
  • 2
    • 0012085727 scopus 로고    scopus 로고
    • Model-checking concurrent systems with unbounded integer variables: Symbolic representations, approximations, and experimental results
    • Bultan T., Gerber R., Pugh W. Model-checking concurrent systems with unbounded integer variables. symbolic representations, approximations, and experimental results ACM Trans. Programming Languages Systems (TOPLAS). 21(4):1999;747-789.
    • (1999) ACM Trans. Programming Languages Systems (TOPLAS) , vol.21 , Issue.4 , pp. 747-789
    • Bultan, T.1    Gerber, R.2    Pugh, W.3
  • 4
    • 4244060600 scopus 로고    scopus 로고
    • Collection des publications de la Faculté des Sciences Appliquées de l'Université de Liège, Liège, Belgium
    • B. Boigelot, Symbolic Methods for Exploring Infinite State Spaces, Collection des publications de la Faculté des Sciences Appliquées de l'Université de Liège, Liège, Belgium, 1999.
    • (1999) Symbolic Methods for Exploring Infinite State Spaces
    • Boigelot, B.1
  • 5
    • 0000157608 scopus 로고
    • On the base-dependence of sets of numbers recognizable by finite automata
    • Cobham A. On the base-dependence of sets of numbers recognizable by finite automata. Math. Systems Theory. 3:1969;186-192.
    • (1969) Math. Systems Theory , vol.3 , pp. 186-192
    • Cobham, A.1
  • 6
    • 0742291838 scopus 로고    scopus 로고
    • Using the astral symbolic model checker as a specification debugger: Three approximation techniques
    • E.M. Clarke, & R.P. Kurshan. New York: IEEE Press
    • Dang Z., Kemmerer R.A. Using the astral symbolic model checker as a specification debugger: Three approximation techniques. Clarke E.M., Kurshan R.P. Proc. 22nd Internat. Conf. on Software Engineering (ICSE 2000). 2000;IEEE Press, New York.
    • (2000) Proc. 22nd Internat. Conf. on Software Engineering (ICSE 2000)
    • Dang, Z.1    Kemmerer, R.A.2
  • 7
    • 84957888220 scopus 로고    scopus 로고
    • Proving safety properties of infinite state systems by compilation into Presburger arithmetic
    • Warsaw, Poland, July 1997, Springer, Berlin
    • L. Fribourg, H. Olsén, Proving safety properties of infinite state systems by compilation into Presburger arithmetic, in: Proc. CONCUR'97, Vol. 1243, Warsaw, Poland, July 1997, Springer, Berlin, 1997, pp. 213-227.
    • (1997) Proc. CONCUR'97 , vol.1243 , pp. 213-227
    • Fribourg, L.1    Olsén, H.2
  • 11
    • 0002217486 scopus 로고
    • Über die Volständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt
    • Warsaw, Poland
    • M. Presburger, Über die Volständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt, in: Comptes Rendus du Premier Congrès des Mathématiciens des Pays Slaves, Warsaw, Poland, 1929, pp. 92-101.
    • (1929) Comptes Rendus du Premier Congrès des Mathématiciens des Pays Slaves , pp. 92-101
    • Presburger, M.1
  • 12
    • 84976676720 scopus 로고
    • The Omega Test: A fast and practical integer programming algorithm for dependence analysis
    • Pugh W. The Omega Test: A fast and practical integer programming algorithm for dependence analysis. Comm. ACM. 35:1992;102-114.
    • (1992) Comm. ACM , vol.35 , pp. 102-114
    • Pugh, W.1
  • 13
    • 0028132512 scopus 로고
    • Counting solutions to Presburger formulas: How and why
    • Pugh W. Counting solutions to Presburger formulas. how and why SIGPLAN. 94-6/94:1994;121-134.
    • (1994) SIGPLAN , vol.94-96 , Issue.94 , pp. 121-134
    • Pugh, W.1
  • 15
    • 0010720433 scopus 로고
    • Presburgerness of predicates regular in two number systems
    • Semenov A.L. Presburgerness of predicates regular in two number systems. Siberian Math. J. 18:1977;289-299.
    • (1977) Siberian Math. J. , vol.18 , pp. 289-299
    • Semenov, A.L.1
  • 16
    • 84863973748 scopus 로고    scopus 로고
    • A comparison of Presburger engines for EFSM reachability
    • Proc. 10th Internat. Conf. on Computer-Aided Verification, Vancouver, June/July 1998, Springer, Berlin
    • T.R. Shiple, J.H. Kukula, R.K. Ranjan, A comparison of Presburger engines for EFSM reachability, in: Proc. 10th Internat. Conf. on Computer-Aided Verification, Lecture Notes in Computer Science, Vol. 1427, Vancouver, June/ July 1998, Springer, Berlin, 1998, pp. 280-292.
    • (1998) Lecture Notes in Computer Science , vol.1427 , pp. 280-292
    • Shiple, T.R.1    Kukula, J.H.2    Ranjan, R.K.3
  • 17
    • 0742326834 scopus 로고
    • Processor allocation and loop scheduling on multiprocessor computers
    • ACM Press, New York
    • N. Tawbi, P. Feautrier, Processor allocation and loop scheduling on multiprocessor computers, in: Proc. 6th Internat. Conf. on Supercomputing, ACM Press, New York, 1992, pp. 63-71.
    • (1992) Proc. 6th Internat. Conf. on Supercomputing , pp. 63-71
    • Tawbi, N.1    Feautrier, P.2
  • 18
    • 0742309194 scopus 로고
    • State space generation with induction
    • Tampere, Finland, June
    • A. Valmari, State space generation with induction, in: Proc. SCAI'89, Tampere, Finland, June 1989, pp. 99-115.
    • (1989) Proc. SCAI'89 , pp. 99-115
    • Valmari, A.1
  • 19
    • 84955609913 scopus 로고
    • An automata-theoretic approach to Presburger arithmetic constraints
    • Proc. Static Analysis Symp., Glasgow, September 1995, Springer, Berlin
    • P. Wolper, B. Boigelot, An automata-theoretic approach to Presburger arithmetic constraints, in: Proc. Static Analysis Symp., Lecture Notes in Computer Science, Vol. 983, Glasgow, September 1995, Springer, Berlin, 1995, pp. 21-32.
    • (1995) Lecture Notes in Computer Science , vol.983 , pp. 21-32
    • Wolper, P.1    Boigelot, B.2
  • 20
    • 84863934422 scopus 로고    scopus 로고
    • On the construction of automata from linear arithmetic constraints
    • Proc. 6th Internat. Conf. on Tools and Algorithms for the Construction and Analysis of Systems, Berlin, March 2000, Springer, Berlin
    • P. Wolper, B. Boigelot, On the construction of automata from linear arithmetic constraints, in: Proc. 6th Internat. Conf. on Tools and Algorithms for the Construction and Analysis of Systems, Lecture Notes in Computer Science, Vol. 1785, Berlin, March 2000, Springer, Berlin, 2000, pp. 1-19.
    • (2000) Lecture Notes in Computer Science , vol.1785 , pp. 1-19
    • Wolper, P.1    Boigelot, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.