We study two extensions of FO 2 [<], first-order logic interpreted in finite words, in which
formulas are restricted to use only two variables. We adjoin to this language two-variable …

Abstract Interval Temporal Logic (ITL) is a flexible notation for both propositional and first-
order reasoning about periods of time found in descriptions of hardware and software …

We consider the two-variable fragment FO^ 2 [<] of first-order logic over finite words.
Numerous characterizations of this class are known. Th\'erien and Wilke have shown that it …

Partially ordered automata are automata where the transition relation induces a partial order
on states. The expressive power of partially ordered automata is closely related to the …

We consider the class of languages defined in the 2-variable fragment of the first-order logic
of the linear order. Many interesting characterizations of this class are known, as well as the …

It is known that the languages definable by formulae of the logics FO^2<,S,2<,S,LTLF,P,X,Y
are exactly the variety DA* D. Automata for this class are not known, nor is its precise …

The variety DA of finite monoids has a huge number of different characterizations, ranging
from two-variable first-order logic FO 2 to unambiguous polynomials. In order to study the …

For two given ω-terms α and β, the word problem for ω-terms over a variety V asks whether
α= β in all monoids in V. We show that the word problem for ω-terms over each level of the …

We give a ranker-based description using finite-index congruences for the variety
$\boldsymbol {\mathrm {DAb}} $ of finite monoids whose regular $\mathcal {D} $-classes …

The wealth of information that is available on the lattice of varieties of bands, is used to
illuminate the structure of the lattice of sub-pseudovarieties of DA, a natural generalization of …