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We investigate the fine-grained and the parameterized complexity of several generalizations of binary constraint satisfaction problems (BINARY-CSPs), that subsume variants of graph colouring problems. Our starting point is the observation…

In this paper, we present a proof of the NP-completeness of computing the smallest Deterministic Finite Automaton (DFA) that distinguishes two given regular languages as DFAs. A distinguishing DFA is an automaton that recognizes a language…

We extend the two-variable logic on data words with guarded regular binary predicates of the form $\widetilde{L}(x,y)$ that is true if positions $x$ and $y$ are in the same class and the factor strictly between $x$ and $y$ is in the regular…

Eilenberg correspondence, based on the concept of syntactic monoids, relates varieties of regular languages with pseudovarieties of finite monoids. Various modifications of this correspondence related more general classes of regular…

We present a Rice-like complexity lower bound for any MSO-definable problem on binary structures succinctly encoded by circuits. This work extends the framework recently developed as a counterpoint to Courcelle's theorem for graphs encoded…

A word is called carefully synchronising for a partial deterministic finite semi-automaton if it maps all states to the same state. Equivalently, it is a composition of partial transformations equal to a constant total transformation. There…

Valence automata are a generalization of various models of automata with storage. Here, each edge carries, in addition to an input word, an element of a monoid. A computation is considered valid if multiplying the monoid elements on the…

Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…

We extend the TFT construction of CFT correlators of [arXiv:hep-th/0204148] to so-called finite logarithmic CFTs for which the algebraic input data is no longer semisimple but still finite. More specifically, starting from the data of a…

We introduce 2-way finite automata with quantum and classical states (2qcfa's). This is a variant on the 2-way quantum finite automata (2qfa) model which may be simpler to implement than unrestricted 2qfa's; the internal state of a 2qcfa…

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…

Let $NFA_b(q)$ denote the set of languages accepted by nondeterministic finite automata with $q$ states over an alphabet with $b$ letters. Let $B_n$ denote the set of words of length $n$. We give a quadratic lower bound on the VC dimension…

A subclass of nondeterministic Finite Automata generated by means of regular Grammars (GFAs, for short) is introduced. A process algebra is proposed, whose semantics maps a term to a GFA. We prove a representability theorem: for each GFA…

In a recent paper we analyzed the space complexity of streaming algorithms whose goal is to decide membership of a sliding window to a fixed language. For the class of regular languages we proved a space trichotomy theorem: for every…

For general input automata, there exist regular constraint languages such that asking if a given input automaton admits a synchronizing word in the constraint language is PSPACE-complete or NP-complete. Here, we investigate this problem for…

We analyze the beta-function equations for string theory in the case when the target space has one spacelike (or timelike) direction and rest is some conformal field theory (CFT) with appropriate central charge and has one nearly marginal…

Non-deterministic Finite Automata (NFA) represent regular languages concisely, increasing their appeal for applications such as word recognition. This paper proposes a new approach to generate NFA from an interaction language such as UML…

A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…

The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…

In this paper, we propose an architecture of oritatami systems with which one can simulate an arbitrary nondeterministic finite automaton (NFA) in a unified manner. The oritatami system is known to be Turing-universal but the simulation…