Around Dot Depth Two

13 years 4 months ago
Around Dot Depth Two
It is known that the languages definable by formulae of the logics FO2[<,S], 2[<,S], LTL[F,P,X,Y] are exactly the variety DAD. Automata for this class are not known, nor is its precise placement within the dot-depth hierarchy of starfree languages. It is easy to argue that 2[<,S] is included in 3[<]; in this paper we show that it is incomparable with B(2)[<], the boolean combination of 2[<] formulae. Using ideas from Straubing's "delay theorem", we extend our earlier work [LPS08] to propose partially-ordered two-way deterministic finite automata with look-around (po2dla) and a new interval temporal logic called LITL and show that they also characterize the variety DAD. We give effective reductions from LITL to equivalent po2dla and from po2dla to equivalent FO2[<,S]. The po2dla automata admit efficient operations of boolean closure and the language non-emptiness of po2dla is NP-complete. Using this, we show that satisfiability of LITL remains NP-comp...
Kamal Lodaya, Paritosh K. Pandya, Simoni S. Shah
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2010
Where DLT
Authors Kamal Lodaya, Paritosh K. Pandya, Simoni S. Shah
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