Over words, two variables are as powerful as one quantifier alternation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An Until hierarchy and other applications of an Ehrenfeucht-Fraïssé game for temporal logic
Information and Computation - Special issue: LICS 1996—Part 1
Varieties Of Formal Languages
Alternating Automata and Logics over Infinite Words
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Partially-Ordered Two-Way Automata: A New Characterization of DA
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
First-order logic with two variables and unary temporal logic
Information and Computation - Special issue: LICS'97
On FO 2 Quantifier Alternation over Words
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Structure theorem and strict alternation hierarchy for FO2 on words
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Unambiguity in timed regular languages: automata and logics
FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
Language theoretical properties of hairpin formations
Theoretical Computer Science
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It is known that the languages definable by formulae of the logics FO2[S], Δ2[S], LTL[F,P,X,Y] are exactly the variety DA*D. 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 Δ2[S] is included in Δ3[2)[2[DA*D. 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-complete assuming a fixed look-around length. (Recall that for LTL[F,X], it is PSPACE-hard.)