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Two-Variable Logic with Two Order Relations

Thomas Schwentick ; Thomas Zeume.

It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete. Actually, EXPSPACE-completeness already holds for structures&nbsp;[&hellip;]

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A Strategy for Dynamic Programs: Start over and Muddle through

Samir Datta ; Anish Mukherjee ; Thomas Schwentick ; Nils Vortmeier ; Thomas Zeume.

In the setting of DynFO, dynamic programs update the stored result of a query whenever the underlying data changes. This update is expressed in terms of first-order logic. We introduce a strategy for constructing dynamic programs that utilises periodic computation of auxiliary data from scratch and&nbsp;[&hellip;]

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Dynamic Complexity of Parity Exists Queries

Nils Vortmeier ; Thomas Zeume.

Given a graph whose nodes may be coloured red, the parity of the number of red nodes can easily be maintained with first-order update rules in the dynamic complexity framework DynFO of Patnaik and Immerman. Can this be generalised to other or even all queries that are definable in first-order logic&nbsp;[&hellip;]

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Register Automata with Extrema Constraints, and an Application to Two-Variable Logic

Szymon Toruńczyk ; Thomas Zeume.

We introduce a model of register automata over infinite trees with extrema constraints. Such an automaton can store elements of a linearly ordered domain in its registers, and can compare those values to the suprema and infima of register values in subtrees. We show that the emptiness problem for&nbsp;[&hellip;]

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