Vojtěch Vorel

Characterization and complexity results on jumping finite automata

In a jumping finite automaton, the input head can jump to an arbitrary position within the remaining input after reading and consuming a symbol. We characterize the corresponding class of languages in terms of special shuffle expressions and survey other equivalent notions from the existing literature. Moreover, we present several results concerning computational hardness and algorithms for parsing and other basic tasks concerning jumping finite automata.

Subset Synchronization and Careful Synchronization of Binary Finite Automata

We present a strongly exponential lower bound that applies both to the subset synchronization threshold for binary deterministic automata and to the careful synchronization threshold for binary partial automata. In the later form, the result finishes the research initiated by Martyugin (2013). Moreover, we show that both the thresholds remain strongly exponential even if restricted to strongly connected binary automata. In addition, we apply our methods to computational complexity. Existence of a subset reset word is known to be PSPACE-complete; we show that this holds even under the restriction to strongly connected binary automata. The results apply also to the corresponding thresholds in two more general settings: D1- and D3-directable nondeterministic automata and composition sequences over finite domains.

Two Results on Discontinuous Input Processing

First, we show that universality and other properties of general jumping finite automata are undecidable, which answers questions asked by Meduna and Zemek in 2012 [12]. Second, we close a study started by Cerno and Mraz in 2010 [3] by proving that a clearing restarting automaton using contexts of length two can accept a binary non-context-free language.

Complexity of Road Coloring with Prescribed Reset Words

By the Road Coloring Theorem (Trahtman, 2008), the edges of any aperiodic directed multigraph with a constant out-degree can be colored such that the resulting automaton admits a reset word. There may also be a need for a particular reset word to be admitted. For certain words it is NP-complete to decide whether there is a suitable coloring of a given multigraph. We present a classification of all words over the binary alphabet that separates such words from those that make the problem solvable in polynomial time. We show that the classification becomes different if we consider only strongly connected multigraphs. In this restricted setting the classification remains incomplete.

An Extremal Series of Eulerian Synchronizing Automata

We present an infinite series of

A lower bound on CNF encodings of the at-most-one constraint

n

Complexity of a problem concerning reset words for Eulerian binary automata

-state Eulerian automata whose reset words have length at least

Complexity of a Problem Concerning Reset Words for Eulerian Binary Automata

(n^2-3)/2

On Basic Properties of Jumping Finite Automata

. This improves the current lower bound on the length of shortest reset words in Eulerian automata. We conjecture that

Parameterized Complexity of Synchronization and Road Coloring

(n^2-3)/2