The extended equivalence problem for a class of non-real-time deterministic pushdown automata

We propose a new class of non-real-time deterministic pushdown automata (dpda's), named dpda's having the weak segmental property (WSP), and show that the equivalence problem is solvable for two dpda's, one of which is in this class. The equivalence checking algorithm to prove this problem is a further extended direct branching algorithm of Tomita; and with the new skipping step combined with the type B′ replacement of Oyamaguchi, Inagaki and Honda. The algorithm is still relatively simple. The class of dpda's given above is one of the widest known subclasses of proper dpda's (introduced by Ukkonen); with the decidable extended equivalence problem.

[1]  Michio Oyamaguchi.  The equivalence problem for real-time DPDAs , 1987, JACM.

[2]  Michio Oyamaguchi.  Some Remarks on Subclass Containment Problems for Several Classes of DPDA's , 1984, Inf. Process. Lett..

[3]  Michael A. Harrison,et al.  Introduction to formal language theory , 1978 .

[4]  Etsuji Tomita,et al.  A Weaker Sufficient Condition for the Equivalence of a Pair of DPDA's to be Decidable , 1985, Theor. Comput. Sci..

[5]  Etsuji Tomita.  A Direct Branching Algorithm for Checking Equivalence of Strict Deterministic VS. LL(k) Grammars , 1983, Theor. Comput. Sci..

[6]  Yasuyoshi Inagaki,et al.  The Equivalence Problem for Two DPDA's, One of Which is a Finite-Turn or One-Counter Machine , 1981, J. Comput. Syst. Sci..

[7]  Amiram Yehudai.  A Hierarchy of Real-Time Deterministic Languages and Their Equivalence , 1982, J. Comput. Syst. Sci..

[8]  Leslie G. Valiant,et al.  Decision procedures for families of deterministic pushdown automata , 1973 .

[9]  Etsuji Tomita.  An Extended Direct Branching Algorithm for Checking Equivalence of Deterministic Pushdown Automata , 1984, Theor. Comput. Sci..

[10]  Etsuji TOMITA,et al.  A Direct Branching Algorithm for Checking the Equivalence of Two Deterministic Pushdown Transducers, one of which is Real-Time Strict , 1989, Theor. Comput. Sci..

[11]  John E. Hopcroft,et al.  Simple Deterministic Languages , 1966, SWAT.

[12]  Etsuji Tomita.  A Direct Branching Algorithm for Checking Equivalence of Some Classes of Deterministic Pushdown Automata , 1982, Inf. Control..

[13]  Amiram Yehudai,et al.  On Equivalence of Grammars Through Transformation Trees , 1979, Theor. Comput. Sci..

[14]  Amiram Yehudai,et al.  New Families of Non Real Time DPDA's and their Decidability Results , 1984, Theor. Comput. Sci..

[15]  Esko Ukkonen.  The equivalence problem for some non-real-time deterministic pushdown automata , 1982, JACM.