Growing Context-Sensitive Languages and Church-Rosser Languages

The growing context-sensitive languages (GCSL) are characterized by a nondeterministic machine model, the so-called shrinking two-pushdown automaton (sTPDA). Then the deterministic version of this automaton (sDTPDA) is shown to characterize the class of generalized Church-Rosser languages (GCRL). Finally, we prove that each growing context-sensitive language is accepted in polynomial time by some one-way auxiliary pushdown automaton with a logarithmic space bound (OW-auxPDA[log, poly]). As a consequence the class of (generalized) Church-Rosser languages and the class of context-free languages are incomparable under set inclusion, which verifies a conjecture of Mc-Naughton et al [MNO88].

[1]  Michal Chytil,et al.  Comparison of the Active Visiting and the Crossing Complexities , 1977, MFCS.

[2]  Ronald V. Book,et al.  Confluent and Other Types of Thue Systems , 1982, JACM.

[3]  Michal Chytil.  Analysis of the Non-Context-Free Component of Formal Languages , 1976, MFCS.

[4]  Neil Immerman,et al.  One-way log-tape reductions , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[5]  Friedrich Otto,et al.  String-Rewriting Systems , 1993, Text and Monographs in Computer Science.

[6]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[7]  Manfred K. Warmuth,et al.  Membership for Growing Context-Sensitive Grammars is Polynomial , 1986, J. Comput. Syst. Sci..

[8]  Ivan Hal Sudborough,et al.  On the Tape Complexity of Deterministic Context-Free Languages , 1978, JACM.

[9]  Daniel A. Walters.  Deterministic Context-Sensitive Languages: Part II , 1970, Inf. Control..

[10]  Seymour Ginsburg,et al.  One-way nondeterministic real-time list-storage languages , 1968, JACM.

[11]  Franz-Josef Brandenburg.  On one-way auxiliary pushdown automata , 1977, Theoretical Computer Science.

[12]  Walter L. Ruzzo,et al.  Tree-size bounded alternation(Extended Abstract) , 1979, J. Comput. Syst. Sci..

[13]  Krzysztof Lorys,et al.  On Growing Context-Sensitive Languages , 1992, ICALP.

[14]  Paliath Narendran,et al.  Church-Rosser Thue systems and formal languages , 1988, JACM.

[15]  Frantisek Mráz,et al.  A Taxonomy of Forgetting Automata , 1993, MFCS.

[16]  Daniel A. Walters,et al.  Deterministic Context-Sensitive Languages , 1969, SWAT.