Alex Kruckman

A Myhill-Nerode theorem for automata with advice

An automaton with advice is a finite state automaton which has access to an additional fixed infinite string called an advice tape. We refine the Myhill-Nerode theorem to characterize the languages of finite strings that are accepted by automata with advice. We do the same for tree automata with advice.

Actions Arising from Intersection and Union

An action is a pair of sets, C and S, and a function

Properly ergodic structures

f:C\times S \rightarrow C

Infinitary Limits of Finite Structures

f:C×S→C. Rothschild and Yalcin gave a simple axiomatic characterization of those actions arising from set intersection, i.e. for which the elements of C and S can be identified with sets in such a way that elements of S act on elements of C by intersection. We introduce and axiomatically characterize two natural classes of actions which arise from set intersection and union. In the first class, the

Higher dimensional obstructions for star reductions.

\uparrow \!\!\downarrow

Model-theoretic dividing lines in least fixed-point logic over finite structures.

↑↓-actions, each element of S is identified with a pair of sets