This report focuses on the following basic decision problems of finite tree automata: nonemptiness and intersection nonemptiness. There is a comprehensive proof of EXPTIME-completeness of the intersection nonemptiness problem, and it is shown that the nonemptiness problem is P-complete. A notion of succinctness is considered with respect to which the intersection nonemptiness problem is in fact a succinct version of the nonemptiness problem. The report includes a short survey of closely related problems which shows that there is a rule of thumb: if a decision problem for (deterministic) finite automata is complete for a certain space complexity then the same decision problem for (deterministic) finite tree automata is complete for the corresponding alternating space complexity, but alternating space is precisely deterministic time, only one exponential higher. 1
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2770
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Introduction to Automata Theory, Language, and Computation
– Hopcroft, Ullman
- 1979
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1587
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Computational Complexity
– Papadimitriou
- 1994
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722
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Rewrite systems
– Dershowitz, Jouannaud
- 1990
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320
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A catalog of complexity classes
– Johnson
- 1990
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192
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Decidability of second-order theories and automata on infinite trees
– Rabin
- 1969
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141
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Tree acceptors and some of their applications
– Doner
- 1970
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141
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Finite automata and their decision problems
– Rabin, Scott
- 1959
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128
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The equivalence problem for regular expressions with squaring requires exponential space
– Meyer, Stockmeyer
- 1972
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112
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Gedanken-experiments on sequential machines
– Moore
- 1956
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93
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Logic programs as types for logic programs
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- 1991
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56
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Complexity of Finitely Presented Algebras
– Kozen
- 1977
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52
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Lower bounds for natural proof systems
– Kozen
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49
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Succinct representations of graphs
– Galperin, Wigderson
- 1983
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48
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Complete problems for deterministic polynomial time, Theoret
– Jones, Laaser
- 1977
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47
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Algebraic automata and context-free sets
– Mezei, Wright
- 1967
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41
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M.: A Note on Succinct Representations of Graphs
– Papadimitriou, Yannakakis
- 1985
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38
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Economy of description by automata, grammars, and formal systems
– Meyer, Fischer
- 1971
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37
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Number of quantifiers is better than number of tape cells
– Immerman
- 1981
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34
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Theorem Proving Using Equational Matings and Rigid E-Unification
– Gallier, Narendran, et al.
- 1992
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27
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Theorem proving using rigid e-unification: Equational matings
– Gallier, Raatz, et al.
- 1987
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24
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Rigid E-unification is NP-complete
– Gallier, Narendran, et al.
- 1988
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21
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A compendium of problems complete for P
– Greenlaw, Hoover, et al.
- 1991
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20
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Embedded implicational dependencies and their inference problem
– Chandra, Lewis, et al.
- 1981
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18
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Bottom-up tree pushdown automata: classification and connection with rewrite systems
– Coquid'e, Dauchet, et al.
- 1994
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18
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On recognizable sets and tree automata
– Courcelle
- 1989
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17
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Simultaneous rigid E-unification is undecidable
– Degtyarev, Voronkov
- 1995
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16
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Limits to Parallel Computation: P -Completeness Theory
– Greenlaw, Hoover, et al.
- 1995
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16
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The complexity of graph problems for succinctly represented graphs
– Balc'azar, Lozano
- 1989
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16
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Word problems — this time with interleaving
– Mayer, Stockmeyer
- 1994
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11
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Rewriting and tree automata
– Dauchet
- 1993
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11
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Herbrand's theorem and equational reasoning: Problems and solutions
– Gurevich, Voronkov
- 1996
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11
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The undecidability of simultaneous rigid E-unification
– Degtyarev, Voronkov
- 1996
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10
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Rigid ~ E-unifiability is DEXPTIME-complete
– Goubault
- 1994
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8
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The decidability of simultaneous rigid E-unification with one variable
– Gurevich, Veanes, et al.
- 1997
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7
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Simultaneous rigid E-unification and related algorithmic problems
– Matiyasevich, Voronkov
- 1996
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6
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The complexity of the inequivalence problem for regular expressions with intersection
– Furer
- 1980
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6
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Tree Automata. Akad'emiai Kiod'o
– G'ecseg, Steinby
- 1984
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4
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Finite automata over finite trees
– Magidor, Moran
- 1969
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2
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The equivalence problem for regular expressions with intersection is not polynomial in tape
– Hunt
- 1973
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1
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Mathematical theory of automata. course notes
– Buchi, Wright
- 1960
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1
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On the Herbrand skeleton problem
– Gurevich, Veanes
- 1997
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1
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Complexity of E0L structural equivalence
– Salomaa, Wood, et al.
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