Abstract
We determine the computational complexity of membership, emptiness and infiniteness for several types ofL systems. TheL systems we consider are ED0L, E0L, EDT0L, and ET0L, with and without empty productions. For each problem and each type of system we establish both upper and lower bounds on the time or memory required for solution by Turing machines.
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References
A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass., 1974.
H. Alt and K. Mehlhorn, Lower bounds for the space complexity of context-free recognition, in S. Michaelson, and R. Milner,Automata, Languages and Programming, (3rd Coll., Edinburgh), University Press, Edinburgh, Scotland, 338–354, 1976.
T. Harju, A polynomial recognition algorithm for the EDT0L languages, Elektro. Inform. Kybernetik 13, 169–177, 1977.
G. T. Herman and G. Rozenberg,Developmental Systems and Languages, North-Holland, Amsterdan, 1975.
J. E. Hopcroft and J. D. Ullman,Formal Languages and their Relation to Automata, Addison-Wesley, Reading, Mass., 1969.
N. D. Jones and W. T Laaser, Complete problems for deterministic polynomial Time,Theoretical Comp. Sci. 3, 105–118, 1976.
N. D. Jones and S. Skyum, Recognition of deterministic ET0L languages in logarithmic space.Information and Control 35, 177–181, 1977.
N. D. Jones and S. Skyum, Complexity of some problems concerningL systems, A. Salomaa and M. Steinby,Automata, Languages and Programming, (4th Coll., Turku), Springer Lecture Notes in Computer Science 52, 301–308, 1977.
P. M. Lewis III R. E. Stearns and J. Hartmanis, Memory bounds for the recognition of context-free and context-sensitive languages,IEEE Conference Record on Switching Circuit Theory and Logical Design, Ann Arbor, Michigan, 191–202, 1965.
A. R. Meyer and L. J. Stockmeyer, The Equivalence problem for regular expressions with squaring requires exponential space,Conf. Rec. 13th Annual IEEE Symposium on Switching and Automata Theory, Baltimore, 125–129, 1972.
J. Seiferas, M. Fischer, and A. Meyer, Refinements of nondeterministic time and space hierarchies,Conf. Rec. 14th Annual IEEE Symposium on Switching and Automata Theory, Iowa, 130–137, 1973.
L. J. Stockmeyer and A. R. Meyer, Word problems requiring exponential time,Proc. 5th Annual ACM Symposium on Theory of Computing, Austin, May 1–9, 1973.
I. H. Sudborough, A note on tape-bounded complexity classes and linear context-free languages,J. ACM 22, 499–500, 1975.
I. H. Sudborough, The time and tape complexity of developmental languages, in: Salomaa, A., Steinby, M.,Automata, Languages and Programming, (4th Coll., Turku), Springer Lecture Notes in Computer Science 52, 509–523, 1977.
L. G. Valiant, General context-free recognition in less than cubic time.J. Computer and Systems Sciences 10, 308–315, 1975.
J. van Leeuwen, Deterministically recognizing E0L languages in timeO(n 3.81). Tech. Rep. Math. Centrum, Amsterdam (1975).
J. van Leeuwen, The membership question for ET0L languages is polynomially complete,Information Processing Letters 3, 138–143, 1975.
J. van Leeuwen, The tape complexity of context-independent developmental languages,J. Computer and Systems Sciences 15, 203–211, 1975.
P. M. B. Vitányi, On the size of D0L languages, in Rozenberg, G. and Salomaa, A. (ed.)L Systems, Springer Lecture Notes in Computer Science 15, 72–77, 1974.
D. H. Younger, Recognition and parsing of context-free languages in Timen 3,Information and Control 10, 189–208, 1967.
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Jones, N.D., Skyum, S. Complexity of some problems concerningL systems. Math. Systems Theory 13, 29–43 (1979). https://doi.org/10.1007/BF01744286
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DOI: https://doi.org/10.1007/BF01744286