Language Equivalence of Deterministic Real-Time One-Counter Automata Is NL-Complete

We prove that deciding language equivalence of deterministic realtime one-counter automata is NL-complete, in stark contrast to the inclusion problem which is known to be undecidable. This yields a subclass of deterministic pushdown automata for which the precise complexity of the equivalence problem can be determined. Moreover, we show that deciding regularity is NL-complete as well.

[1]  Géraud Sénizergues,et al.  L(A)=L(B)? A simplified decidability proof , 2002, Theor. Comput. Sci..

[2]  Jirí Srba,et al.  Height-Deterministic Pushdown Automata , 2007, MFCS.

[3]  Emily P. Friedman.  The Inclusion Problem for Simple Languages , 1976, Theor. Comput. Sci..

[4]  Faron Moller,et al.  A Polynomial Algorithm for Deciding Bisimilarity of Normed Context-Free Processes , 1994, Theor. Comput. Sci..

[5]  Piotr Berman,et al.  Learning one-counter languages in polynomial time , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[6]  Faron Moller,et al.  Simulation Problems for One-Counter Machines , 1999, SOFSEM.

[7]  Ken Higuchi,et al.  A Polynomial-Time Algorithm for Checking the Inclusion for Real-Time Deterministic Restricted One-Counter Automata Which Accept by Final State , 1995, IEICE Trans. Inf. Syst..

[8]  Faron Moller,et al.  Simulation and Bisimulation over One-Counter Processes , 2000, STACS.

[9]  Ken Higuchi,et al.  A Polynomial-Time Algorithm for Checking the Inclusion for Real-Time Deterministic Restricted One-Counter Automata Which Accept by Accept Mode , 1998 .

[10]  Amr F. Fahmy,et al.  Efficient Learning of Real Time One-Counter Automata , 1995, ALT.

[11]  Piotr Berman,et al.  Learning One-Counter Languages in Polynomial .Time (Extended Abstract) , 1987, FOCS 1987.

[12]  Richard Mayr.  Undecidability of Weak Bisimulation Equivalence for 1-Counter Processes , 2003, ICALP.

[13]  Piotr Berman,et al.  Deciding equivalence of deterministic one-counter automata in polynomial time with applications to learning , 1988 .

[14]  Didier Caucal.  Synchronization of Pushdown Automata , 2006, Developments in Language Theory.

[15]  Stanislav Böhm,et al.  Bisimilarity of One-Counter Processes Is PSPACE-Complete , 2010, CONCUR.

[16]  Leslie G. Valiant,et al.  Deterministic One-Counter Automata , 1975, J. Comput. Syst. Sci..

[17]  Géraud Sénizergues,et al.  L(A) = L(B) ? decidability results from complete formal systems , 2001 .

[18]  M. Minsky.  Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing Machines , 1961 .

[19]  Petr Jancar,et al.  Decidability of Bisimilarity for One-Counter Processes , 2000, Inf. Comput..

[20]  Rajeev Alur,et al.  Visibly pushdown languages , 2004, STOC '04.

[21]  Faron Moller,et al.  DP lower bounds for equivalence-checking and model-checking of one-counter automata , 2004, Inf. Comput..

[22]  Géraud Sénizergues,et al.  The Equivalence Problem for t-Turn DPDA Is Co-NP , 2003, ICALP.

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

[24]  Neil Immerman.  Nondeterministic Space is Closed Under Complementation , 1988, SIAM J. Comput..

[25]  Colin Stirling,et al.  Deciding DPDA Equivalence Is Primitive Recursive , 2002, ICALP.