Related papers: Computational complexity of problems for determini…
We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond…
An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…
Topological behavior, such as chaos, irreducibility, and mixing of a one-sided shift of finite type, is well elucidated. Meanwhile, the investigation of multidimensional shifts, for instance, textile systems is difficult and only a few…
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
Influence diagrams allow for intuitive and yet precise description of complex situations involving decision making under uncertainty. Unfortunately, most of the problems described by influence diagrams are hard to solve. In this paper we…
Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full…
Systems obtained by quotienting a subshift of finite type (SFT) by another SFT are called finitely presented in the literature. Analogously, if a sofic shift is quotiented by a sofic equivalence relation, we call the resulting system…
We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable…
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of model checking a fixed monadic second-order formula over evolving subgraphs of a fixed maximal…
In this paper we study the shifts, which are the shift-invariant and topologically closed sets of configurations over a finite alphabet in $\mathbb{Z}^d$. The minimal shifts are those shifts in which all configurations contain exactly the…
A synchronizing word of a deterministic automaton is a word in the alphabet of colors of its edges that maps the automaton to a single state. A coloring of edges of a directed graph is synchronizing if the coloring turns the graph into a…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
In this manuscript we study properties of multidimensional shifts. More precisely, we study the necessary and sufficient conditions for a shift to be sofic, i.e. the boundary between sofic shifts and effective ones. To this end, we use…
We study constraint satisfaction problems (CSPs) where the constraint languages are defined by finite automata, giving rise to automata-based CSPs. The key notion is the concept of Automatic Constraint Satisfaction Problem ($AutCSP$), where…
An algebraic telic problem is a decision problem in $\textsf{NP}_\mathbb{R}$ formalizing finite-time reachability questions for one-dimensional dynamical systems. We prove that the existence of "natural" mapping reductions between algebraic…
In recent years, there has been increasing interest in explanation methods for neural model predictions that offer precise formal guarantees. These include abductive (respectively, contrastive) methods, which aim to compute minimal subsets…
We study the density of periodic configurations for shift spaces defined on (the Cayley graph of) a finitely generated group. We prove that in the case of a full shift on a residually finite group and in that of a group shift space on an…