TL;DR
A new class of automata running on infinite trees of arbitrary arity is introduced, and several algorithms to perform classical operations are developed for those automata and precisely characterise their complexities.
Higher-Dimensional Automata (HDAs) provide a geometric model of true concurrency. While hereditary history-preserving (hhp) bisimilarity is the finest behavioural equivalence in van Glabbeek's spectrum, no modal logic has previously characterised it on HDAs. We introduce several new intermediate equivalences that sit s...
We survey selected open problems in the theory of synchronizing automata, centered around the famous Černý conjecture. A deterministic finite automaton is called synchronizing if it admits a reset word whose action maps all states to a single state. The Černý conjecture states that every synchronizing automaton wit...
We investigate the computational complexity of analyzing the structural and behavioral properties of deterministic k-pebble automata, which represent a natural framework for studying minimal programmable machines. First, we provide an explicit construction of a three-pebble automaton U capable of simulating any determi...
This work considers a definitional fragment of Temporal Equilibrium Logic, which allows to capture temporal rules that contain complex (implication-free) temporal formulas in rule bodies, and shows how the set of all stable models of a theory can be represented as a non-deterministic finite state automaton (NFA).
Motivated by educational applications, we study the problem of computing all corrections that transform a finite automaton into one recognizing a given regular language L. We show that for deterministic finite automata the set of all corrections can be finitely characterized as a regular tree language. The construction...
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