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On exponential-time completeness of the circularity problem for attribute grammars

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Pei-Chi WuAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 26, Issue 1

Pages 186 - 190

https://doi.org/10.1145/963778.963783

Published: 01 January 2004 Publication History

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Abstract

Attribute grammars (AGs) are a formal technique for defining semantics of programming languages. Existing complexity proofs on the circularity problem of AGs are based on automata theory, such as writing pushdown acceptor and alternating Turing machines. They reduced the acceptance problems of above automata, which are exponential-time (EXPTIME) complete, to the AG circularity problem. These proofs thus show that the circularity problem is EXPTIME-hard, at least as hard as the most difficult problems in EXPTIME. However, none has shown that the problem is EXPTIME-complete. This paper presents an alternating Turing machine for the circularity problem. The alternating Turing machine requires polynomial space. Thus, the circularity problem is in EXPTIME and is then EXPTIME-complete.

References

[1]

Chandra, A. K., Kozen, D. C., and Stockmeyer, L. J. 1981. Alternation. J. ACM 28, 1 (Jan.), 114--133.

Digital Library

Google Scholar

[2]

Deransart, P., Jourdan, M., and Lorho, B. 1984. Speeding up circularity tests for attribute grammars. Acta Informatica 21, 375--391.

Crossref

Google Scholar

[3]

DILL, J. M. 1989. A counterexample for 'A simpler construction for showing the intrinsically exponential complexity of the circularity problem for attribute grammars.' J. ACM 36, 1 (Jan.), 92--96.

Digital Library

Google Scholar

[4]

Gray, R. W., Heuring, V. P., Levi, S. P., Sloane, A. W., and Waite, W. M. 1992. Eli: A complete, flexible compiler construction system. Commun. ACM 35, 2 (Feb.), 121--131.

Digital Library

Google Scholar

[5]

Jazayeri, M., Ogden, W. F., and Rounds, W. C. 1975. The intrinsically exponential complexity of the circularity problem for attribute grammars. Commun. ACM 18, 12 (Dec.), 697--706.

Digital Library

Google Scholar

[6]

JAzayeri, M. 1981. A simpler construction for showing the intrinsically exponential complexity of the circularity problem for attribute grammars. J. ACM 28, 4 (Oct.), 715--720.

Digital Library

Google Scholar

[7]

Jones, N. D. 1980. Circularity testing of attribute grammars requires exponential time: A simpler proof. Tech. rep. DAIMI PB-107. Computer Science Department, Aarhus University, Aarhus, Denmark.

Google Scholar

[8]

Knuth, D. E. 1968. Semantics of context-free languages. Math. Syst. Theory 2, 2, 127--145. Correction: Knuth, D. E. 1971. Math. Syst, Theory 5, 1, 95--96.

Crossref

Google Scholar

[9]

Räihä, K.-J., and Saarinen, M. 1982. Testing attribute grammars for circularity. Acta Informatica 17, 185--192.

Digital Library

Google Scholar

[10]

Reps, T., and Teitelbaum, T. 1989. The Synthesizer Generator: A System for Constructing Language-Based Editors. Springer-Verlag, New York, NY.

Digital Library

Google Scholar

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Cohen TGil JMaman I(2006)JTLACM SIGPLAN Notices10.1145/1167515.116748141:10(89-108)Online publication date: 16-Oct-2006
https://dl.acm.org/doi/10.1145/1167515.1167481
Cohen TGil JMaman ITarr PCook WBiddle RGabriel R(2006)JTLProceedings of the 21st annual ACM SIGPLAN conference on Object-oriented programming systems, languages, and applications10.1145/1167473.1167481(89-108)Online publication date: 23-Oct-2006
https://dl.acm.org/doi/10.1145/1167473.1167481

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cover image ACM Transactions on Programming Languages and Systems

ACM Transactions on Programming Languages and Systems Volume 26, Issue 1

January 2004

220 pages

ISSN:0164-0925

EISSN:1558-4593

DOI:10.1145/963778

Issue’s Table of Contents

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Published: 01 January 2004

Published in TOPLAS Volume 26, Issue 1

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Cohen TGil JMaman I(2006)JTLACM SIGPLAN Notices10.1145/1167515.116748141:10(89-108)Online publication date: 16-Oct-2006
https://dl.acm.org/doi/10.1145/1167515.1167481
Cohen TGil JMaman ITarr PCook WBiddle RGabriel R(2006)JTLProceedings of the 21st annual ACM SIGPLAN conference on Object-oriented programming systems, languages, and applications10.1145/1167473.1167481(89-108)Online publication date: 23-Oct-2006
https://dl.acm.org/doi/10.1145/1167473.1167481

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The intrinsically exponential complexity of the circularity problem for attribute grammars

Sublogarithmic Space-Bounded Multi-Inkdot Alternating Turing Machines with Only Existential (Universal) States

The Complexity of Szilard Languages of Matrix Grammars Revisited

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