Related papers: Finite automata for testing uniqueness of Eulerian…
We define train track maps for graphs-of-groups $\cal G$ and exhibit the precise conditions under which the fundamental finiteness properties known for classical train track maps extend to this generalization. These finiteness properties…
Finitary Idealized Concurrent Algol (FICA) is a prototypical programming language combining functional, imperative, and concurrent computation. There exists a fully abstract game model of FICA, which in principle can be used to prove…
We consider finite two-way automata and measure the use of two-way motion by counting the number of left moves in accepting computations. Restriction of the automata according to this measure allows us to study in detail the use of two-way…
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…
We introduce a new tool, called the orbit automaton, that describes the action of an automaton group $G$ on the subtrees corresponding to the orbits of $G$ on levels of the tree. The connection between $G$ and the groups generated by the…
We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…
This paper considers finite-automata based algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this…
In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…
We describe some necessary conditions for the existence of a Hamiltonian path in any graph (in other words, for a graph to be traceable). These conditions result in a linear time algorithm to decide the Hamiltonian path problem for cactus…
In this paper we deal with verification of safety properties of term-rewriting systems. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which further resolved by…
We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed…
We prove that an eulerian graph $G$ admits a decomposition into $k$ closed trails of odd length if and only if and it contains at least $k$ pairwise edge-disjoint odd circuits and $k\equiv |E(G)|\pmod{2}$. We conjecture that a connected…
We investigate the (non)-existence of universal automata for some classes of automata, such as finite automata and pushdown automata, and in particular the influence of the representation and encoding function. An alternative approach,…
We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…
This short note aims at proving that the isolation problem is undecidable for probabilistic automata with only one probabilistic transition. This problem is known to be undecidable for general probabilistic automata, without restriction on…
A \emph{data automaton} is a finite automaton equipped with variables (counters or registers) ranging over infinite data domains. A trace of a data automaton is an alternating sequence of alphabet symbols and values taken by the counters…
Singularity in robot controls is an important problem. By identifying an appropriate trajectory for the robots, the singular situations can be avoided. In this paper an identification algorithm is proposed to control the robot such that it…