Abstract:
In [Saf88] an exponential determinization procedure for Buchi automata was shown, yielding tight bounds for decision procedures of some logics ([EJ88, Saf88, SV89, KT89]). In [SV89] the complexity of determinization and complementation of !-automata was further investigated, leaving as an open question the complexity of the determinization of a single class of !-automata. For this class of !-automata with strong fairness as acceptance condition (Streett automata), [SV89] managed to show an exponential complementation procedure, however the blow-up of translating these automata, to any of the classes known to admit exponential determinization, is inherently exponential. This might suggest that the blow-up of the determinization of Streett automata is inherently doubly exponential. This paper shows an exponential determinization construction for Streett automata. In fact, the complexity of our construction is roughly the same as the complexity achieved in [Saf88] for Buchi ...
Citations
|
1309
|
The Temporal Logic of Reactive and Concurrent Systems: Specification
– Manna, Pnueli
- 1991
|
|
453
|
and P.Wolper. An Automata-Theoretic approach to Automatic Program Verification
– Vardi
- 1986
|
|
260
|
On the development of reactive systems
– Harel, Pnueli
- 1985
|
|
200
|
Decidability of second-order theories and automata on innite trees
– Rabin
- 1969
|
|
170
|
Automatic verification of probabilistic concurrent finite-state programs
– Vardi
- 1987
|
|
168
|
Automata-theoretic techniques for modal logic of programs
– Vardi, Wolper
- 1986
|
|
154
|
Tree automata, mu-calculus, and determinacy
– Emerson, Jutla
- 1991
|
|
120
|
Logics of program
– Kozen, Tiurzyn
- 1990
|
|
115
|
The complexity of tree automata and logics of programs
– Emerson, Jutla
- 1988
|
|
80
|
Solving sequential conditions by finite-state strategies
– Büchi, Landweber
- 1969
|
|
68
|
On the complexity of !-automata
– Safra
- 1988
|
|
67
|
Testing and generating infinite sequences by a finite automaton
– McNaughton
- 1966
|
|
39
|
Deciding Full Branching Time Logic
– Emerson, Sistla
- 1984
|
|
34
|
Propositional Dynamic Logic of Looping and Converse is Elementary Decidable
– Streett
- 1982
|
|
29
|
Weakly definable relations and special automata
– Rabin
- 1970
|
|
28
|
Infinite sequences on finite machines
– Muller
- 1963
|
|
26
|
Improved upper and lower bounds for modal logics of programs
– Vardi, Stockmeyer
- 1985
|
|
23
|
Weak monadic second order theory of successor is not elementary recursive
– Meyer
- 1975
|
|
16
|
Progress measures, immediate determinacy, and a subset construction for tree automata
– Klarlund
- 1994
|
|
16
|
On ω-automata and temporal logic
– Safra, Vardi
- 1989
|
|
11
|
Progress measures for complementation of !-automata with applications to temporal logic
– Klarlund
- 1991
|
|
3
|
The complementation problem for Buchi autamata with application to temporal logic
– Sistla, Vardi, et al.
- 1987
|
|
1
|
On a decision method in resricted second order arithmetics
– Buchi
- 1960
|
|
1
|
On the complementation of buchi autamata
– Pecuchet
- 1986
|
