An automata-theoretic algorithm for counting solutions to Presburger formulas

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

Volumn 2985, Issue , 2004, Pages 104-119

  Parker, Erin ^a   Chatterjee, Siddhartha ^b  

^a Brooks Computer Science Building   (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS;

BINARY REPRESENTATIONS; COUNTING SOLUTIONS TO PRESBURGER FORMULAS; DETERMINISTIC FINITE AUTOMATA; FREE VARIABLE; INTEGER SOLUTIONS; PRESBURGER;

FINITE AUTOMATA;

EID: 24644524767     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24723-4_8     Document Type: Article

References (31)

1. Clauss, P.: Counting solutions to linear and nonlinear constraints through Ehrhart polynomials: Applications to analyze and transform scientific programs. In: Proceedings of the 1996 ACM International Conference on Supercomputing. (1996) 278-285
2. Ferrante, J., Sarkar, V., Thrash, W.: On estimating and enhancing cache effectiveness. In Banerjee, U., et al., eds.: Proceedings of the Fourth Annual Workshop on Programming Languages and Compilers for Parallel Computing. Volume 589 of Lecture Notes in Computer Science., Springer (1991) 328-343
3. Chatterjee, S., Parker, E., Hanlon, P.J., Lebeck, A.R.: Exact analysis of the cache behavior of nested loops. In: Proceedings of 2001 ACM SIGPLAN Conference on Programming Language Design and Implementation. (2001) 286-297
4. Ghosh, S., Martonosi, M., Malik, S.: Cache miss equations: A compiler framework for analyzing and tuning memory behavior. ACM Transactions on Programming Languages and Systems 21 (1999) 703-746
5. Haghighat, M., Polychronopoulos, C.: A basis for parallelization, optimization and scheduling of programs. Technical Report 1317, CSRD, University of Illinois (1993)
6. Haghighat, M., Polychronopoulos, C.: Symbolic analysis: A basis for parallelization, optimization and scheduling of programs. In Banerjee, U., et al., eds.: Proceedings of the Sixth Annual Workshop on Programming Languages and Compilers for Parallel Computing. Volume 768 of Lecture Notes in Computer Science., Springer (1993) 567-585
7. Tawbi, N.: Estimation of nested loop exection time by integer arithmetics in convex polyhedra. In: Proceedings of the Eighth International Parallel Processing Symposium. (1994) 217-221
8. Tawbi, N., Feautrier, P.: Processor allocation and loop scheduling on multiprocessor computers. In: Proceedings of the 1992 ACM International Conference on Supercomputing. (1992) 63-71
9. Pugh, W.: Counting solutions to Presburger formulas: How and why. In: Proceedings of 1994 ACM SIGPLAN Conference on Programming Language Design and Implementation. (1994) 121-134
10. Ehrhart, E.: Polynômes arithmétiques et Méthode des Polyédres en Combinatoire. Volume 35 of International Series of Numerical Mathematics. Birkhäuser Verlag, Basel/Stuttgart (1977)
11. Loechner, V.: PolyLib: A Library for Manipulating Parameterized Polyhedra. (1999)
12. Fricker, C., Temam, O., Jalby, W.: Influence of cross-interference on blocked loops: A case study with matrix-vector multiply. ACM Transactions on Programming Languages and Systems 17 (1995) 561-575
13. Barvinok, A.I.: A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed. Mathematics of Operations Research 19 (1994) 769-779
14. Dyer, M., Kannan, R.: On Barvinok's algorithm for counting lattic points in fixed dimension. Mathematics of Operations Research 22 (1997) 545-549
15. Loera, J.A.D., Hemmecke, R., Tauzer, J., Yoshida, R.: Effective lattice point counting in rational convex polytopes. http://www.math.ucdavis.edu/~latte/ pdf/lattE.pdf (2003)
16. Presburger, M.: Über die Vollständigkeit 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. (1929) 92-101
17. 22pn upper bound on the complexity of Presburger arithmetic. Journal of Computer and System Sciences 16 (1978) 323-332
18. Weispfenning, V.: Complexity and uniformity of elimination in Presburger arithmetic. In: Proceedings of the 1997 ACM SIGSAM International Symposium on Symbolic and Algebraic Computation. (1997) 48-53
19. Büchi, J.R.: Weak second-order arithmetic and finite automata. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 6 (1960) 66-92
20. Büchi, J.R.: On a decision method in restricted second-order arithmetic. In Nagel, E., et al., eds.: Proceedings of the International Congress on Logic, Methodology and Philosophy of Science 1960, Stanford University Press (1962) 1-11
21. Boudet, A., Comon", H.: Diophantine equations, Presburger arithmetic and finite automata. In Kirchner, H., ed.: Proceedings of 21st International Colloquium on Trees in Algebra and Programming. Volume 1059 of Lecture Notes in Computer Science., Springer (1996) 30-43
22. Bartzis, C., Bultan, T.: Efficient symbolic representations for arithmetic constraints in verification. Technical Report 2002-16, Computer Science Department, University of California, Santa Barbara (2002)
23. Bartzis, C., Bultan, T.: Automata-based representations for arithmetic constraints in automated verification. In: Proceedings of the 7th International Conference on Implementation and Application of Automata. (2002) 282-288
24. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley Publishing Company (1979)
25. Boigelot, B., Wolper, P.: Representing arithmetic constraints with finite automata: An overview. In J.Stuckey, P., ed.: Proceedings of the 18th International Conference on Logic Programming. Volume 2401 of Lecture Notes in Computer Science., Springer (2002) 1-19
26. Wolper, P., Boigelot, B.: An automata-theoretic approach to Presburger arithmetic constraints (extended abstract). In Mycroft, A., ed.: Proceedings of the Second International Static Analysis Symposium. Volume 983 of Lecture Notes in Computer Science., Springer (1995) 21-32
27. Wolper, P., Boigelot, B.: On the construction of automata from linear arithmetic constraints. In Graf, S., Schwartzbach, M.L, eds.: Proceedings of the Sixth International Conference on Tools and Algorithms for Construction and Analysis of Systems. Volume 1785 of Lecture Notes in Computer Science., Springer (2000) 1-19
28. Klarlund, N., Møller, A.: MONA Version 1.4 User Manual. (2001) http://www.brics.dk/mona.
29. Parker, E., Chatterjee, S.: An automata-theoretic algorithm for counting solutions to Presburger formulas. Technical Report TR04-001, Department of Computer Science, University of North Carolina at Chapel Hill (2004)
30. Kelly, W., Maslov, V., Pugh, W., Rosser, E., Shpeisman, T., Wonnacott, D.: The Omega Calculator and Library, Version 1.1.0. (1996) http://www.cs.umd. edu/projects/omega.
31. Kelly, W., Maslov, V., Pugh, W., Rosser, E., Shpeisman, T., Wonnacott, D.: The Omega Library Version 1.1.0 Interface Guide. (1996) http://www.cs.umd. edu/projects/omega.