Alternation

Journal of the ACM - Tập 28 Số 1 - Trang 114-133 - 1981
Ashok K. Chandra1, Dexter Kozen1, Larry J. Stockmeyer1
1IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York

Tóm tắt

Từ khóa


Tài liệu tham khảo

AHO , A.V. , HOPCROFT , J.E. , AND ULLMAN , J.D. The Design and Analysis of Computer Algorithms . Addison-Wesley , Reading, Mass ., 1974 . AHO, A.V., HOPCROFT, J.E., AND ULLMAN, J.D. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass., 1974.

HERMAN , L. Precise bounds for Presburger arithmetic and the reals with addition . Proc. 18th IEEE Symp. on Foundations of Computer Science, Providence, R.I. , 1977 , pp. 95 - 99 . HERMAN, L. Precise bounds for Presburger arithmetic and the reals with addition. Proc. 18th IEEE Symp. on Foundations of Computer Science, Providence, R.I., 1977, pp. 95-99.

BORODIN A. Personal communication. BORODIN A. Personal communication.

CHANDRA , A.K. , AND STOCKMEYER , L.J. Alternation. Proc. 17th 1EEE Symp. on Foundations of Computer Science , Houston, Texas , 1976 , pp. 98 - 108 . CHANDRA, A.K., AND STOCKMEYER, L.J. Alternation. Proc. 17th 1EEE Symp. on Foundations of Computer Science, Houston, Texas, 1976, pp. 98-108.

COOK , S.A. The complexity of theorem proving procedures . Proc. 3rd ACM Symp. on Theory of Computing , Shaker Heights, Ohio , 1971 , pp. 151 - 158 . 10.1145/800157.805047 COOK, S.A. The complexity of theorem proving procedures. Proc. 3rd ACM Symp. on Theory of Computing, Shaker Heights, Ohio, 1971, pp. 151-158. 10.1145/800157.805047

FISCHER , M.J. , AND LADNER , R.E . Propositional dynamic logic of regular programs . J. Comput. Syst. Sci. 18 , 2 ( 1979 ), 194-211. FISCHER, M.J., AND LADNER, R.E. Propositional dynamic logic of regular programs. J. Comput. Syst. Sci. 18, 2 (1979), 194-211.

GOLDSCHLAGER , L.M. A unified approach to models of synchronous parallel machines . Proc. 10th ACM Symp. on Theory of Computing , San Diego, Calif. 1978 , pp. 89 - 94 . 10.1145/800133.804336 GOLDSCHLAGER, L.M. A unified approach to models of synchronous parallel machines. Proc. 10th ACM Symp. on Theory of Computing, San Diego, Calif. 1978, pp. 89-94. 10.1145/800133.804336

HARTMANIS , J. , AND HUNT , H.B. III. The LBA problem and its importance in the theory of computing . In Complexity of Computation , R.M. Karp, Ed., American Mathematical Society , Providence, R.I. , 1974 , pp. 1 - 26 . HARTMANIS, J., AND HUNT, H.B. III. The LBA problem and its importance in the theory of computing. In Complexity of Computation, R.M. Karp, Ed., American Mathematical Society, Providence, R.I., 1974, pp. 1-26.

HARTMANIS , J. , AND SIMON , J. On the power of multiplication in random access machines . Proc. 15th IEEE Symp. on Switching and Automata Theory, New Orleans, La. , 1974 , pp. 13 - 23 . HARTMANIS, J., AND SIMON, J. On the power of multiplication in random access machines. Proc. 15th IEEE Symp. on Switching and Automata Theory, New Orleans, La., 1974, pp. 13-23.

HOPCROFT , J.E. , AND ULLMAN , J.D. Formal Languages and their Relation to Automata . Addison- Wesley , Reading, Mass ., 1969 . HOPCROFT, J.E., AND ULLMAN, J.D. Formal Languages and their Relation to Automata. Addison- Wesley, Reading, Mass., 1969.

KARP , R.M. Reducibility among combinatorial problems . In Complexity of Computer Computations , R. E. Miller and J. W. Thatcher, Eds., Plenum Press , New York , 1972 , pp. 85 - 104 . KARP, R.M. Reducibility among combinatorial problems. In Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, Eds., Plenum Press, New York, 1972, pp. 85-104.

KASA'I , T. , ADACHI , A. , AND 1WATA, S. Classes of pebble games and complete problems. SIAM J. Comput. 8 ( 1979 ), 574 - 586 . KASA'I, T., ADACHI, A., AND 1WATA, S. Classes of pebble games and complete problems. SIAM J. Comput. 8 (1979), 574-586.

KOZEN , D. On parallelism in Turing machines . Proc. 17th IEEE Symp. on Foundations of Computer Science , Houston, Texas , 1976 , pp. 89 - 97 . KOZEN, D. On parallelism in Turing machines. Proc. 17th IEEE Symp. on Foundations of Computer Science, Houston, Texas, 1976, pp. 89-97.

KOZEN , D. Complexity of Boolean algebras. Theoret. Comput. ScL I0 ( 1980 ), 221-247. KOZEN, D. Complexity of Boolean algebras. Theoret. Comput. ScL I0 (1980), 221-247.

LADNER , R.E. , LIPTON , R.J. , AND STOCKMEYER , L.J. Alternating pushdown automata . Proc. 19th 1EEE Symp. on Foundations of Computer Science , Ann Arbor, Mich. , 1978 . LADNER, R.E., LIPTON, R.J., AND STOCKMEYER, L.J. Alternating pushdown automata. Proc. 19th 1EEE Symp. on Foundations of Computer Science, Ann Arbor, Mich., 1978.

MEYER , A.R. , AND FISCHER , M.J. Economy of description of automata, grammars, and formal systems . Proc. 12th IEEE Symp. on Switching and Automata Theory, East Lansing, Mich. , 1971 , pp. 188 - 191 . MEYER, A.R., AND FISCHER, M.J. Economy of description of automata, grammars, and formal systems. Proc. 12th IEEE Symp. on Switching and Automata Theory, East Lansing, Mich., 1971, pp. 188-191.

PRATT , V.R. , AND STOCKMEYER , L.J . A characterization of the power of vector machines . J. Comput. Syst. ScL 12 ( 1976 ), 198 - 221 . PRATT, V.R., AND STOCKMEYER, L.J. A characterization of the power of vector machines. J. Comput. Syst. ScL 12 (1976), 198-221.

RABIN , M.O. , AND SCOTT , D . Finite automata and their decision problems . IBM J. Res. Dev. 3 ( 1959 ), 115 - 125 . RABIN, M.O., AND SCOTT, D. Finite automata and their decision problems. IBM J. Res. Dev. 3 (1959), 115-125.

Rozzo, W. L. General context-free language recognition. Ph.D. Diss ., Computer Science Division, Univ. of California , Berkeley, Calif ., 1978 . Rozzo, W.L. General context-free language recognition. Ph.D. Diss., Computer Science Division, Univ. of California, Berkeley, Calif., 1978.

SAVITCH , W.J . Relationships between nondeterministic and deterministic tape complexities . J. Comput. Syst. Sci 4 ( 1970 ), 177 - 192 . SAVITCH, W.J. Relationships between nondeterministic and deterministic tape complexities. J. Comput. Syst. Sci 4 (1970), 177-192.

SAVITCH , W.J. , AND STIMSON , M.J. The complexity of time bounded recursive computations . Proc. 1976 Johns Hopkins Conf. on Information Sciences and Systems , Baltimore, Md. , pp. 42 - 46 . SAVITCH, W.J., AND STIMSON, M.J. The complexity of time bounded recursive computations. Proc. 1976 Johns Hopkins Conf. on Information Sciences and Systems, Baltimore, Md., pp. 42-46.

SCOTT , D. Outline of a mathematical theory of computation . Proc. 4th Ann. Princeton Conf. on Information Sciences and Systems , Princeton, N. J. 1970 , pp. 169 - 176 . SCOTT, D. Outline of a mathematical theory of computation. Proc. 4th Ann. Princeton Conf. on Information Sciences and Systems, Princeton, N. J. 1970, pp. 169-176.

SIMON , J. On feasible numbers . Proc. 9th ACM Symp. on Theory of Computing, Boulder, Colo. , 1977 , pp. 195 - 207 . 10.1145/800105.803409 SIMON, J. On feasible numbers. Proc. 9th ACM Symp. on Theory of Computing, Boulder, Colo., 1977, pp. 195-207. 10.1145/800105.803409

STOCKMEYER , L.J . The polynomial-time hierarchy . Theoret. Comput. ScL 3 ( 1977 ), 1 - 22 . STOCKMEYER, L.J. The polynomial-time hierarchy. Theoret. Comput. ScL 3 (1977), 1-22.

STOCKMEYER , L.J. , AND CHANDRA , A.K . Provably difficult combinatorial games . SIAM J. Comput. 8 ( 1979 ), 151 - 174 . STOCKMEYER, L.J., AND CHANDRA, A.K. Provably difficult combinatorial games. SIAM J. Comput. 8 (1979), 151-174.

STOCKMEYER , L.J. , AND MEYER , A.R. Word problems requiring exponentialtime: Preliminary report . Proc. 5th ACM Symp. on Theory of Computing , Austin, Texas , 1973 , pp. 1 - 9 . 10.1145/800125.804029 STOCKMEYER, L.J., AND MEYER, A.R. Word problems requiring exponentialtime: Preliminary report. Proc. 5th ACM Symp. on Theory of Computing, Austin, Texas, 1973, pp. 1-9. 10.1145/800125.804029

WRATHALL , C . Complete sets and the polynomial-time hierarchy . Theoret. Comput. ScL 3 ( 1977 ), 23 - 34 . WRATHALL, C. Complete sets and the polynomial-time hierarchy. Theoret. Comput. ScL 3 (1977), 23-34.