Related papers: Algebraic and Combinatorial Tools for State Comple…

I study the state complexity of binary operations on regular languages over different alphabets. It is well known that if $L'_m$ and $L_n$ are languages restricted to be over the same alphabet, with $m$ and $n$ quotients, respectively, the…

A common technique for checking properties of complex state machines is to build a finite abstraction then check the property on the abstract system -- where a passing check on the abstract system is only transferred to the original system…

Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the…

We introduce a monotone to quantify the amount of non-stabilizerness (or magic for short), in an arbitrary quantum state. The monotone gives a necessary and sufficient criterion for detecting the presence of magic for both pure and mixed…

We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a…

Voting theory has become increasingly integrated with computational social choice and multiagent systems. Computational complexity has been extensively used as a shield against manipulation of voting systems, however for several voting…

Most theoretical definitions about the complexity of manipulating elections focus on the decision problem of recognizing which instances can be successfully manipulated, rather than the search problem of finding the successful manipulative…

Neutron stars are unique laboratories to probe matter in extreme conditions, not accessible in terrestrial laboratories. Here, we discuss the modelling of the neutron-star equation of state, particularly in connection with recent…

Magic states can be used as a resource to circumvent the restrictions due to stabilizer-preserving operations, and magic-state conversion has not been studied in the single-copy regime thus far. Here we solve the question of whether a…

Given a countable set X (usually taken to be the natural numbers or the integers), an infinite permutation \pi of X is a linear ordering of X. This paper investigates the combinatorial complexity of the infinite permutation on the natural…

People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…

In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying the so-called factor complexity of infinite sequences, which…

This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row…

Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose…

Monoidal computer is a categorical model of intensional computation, where many different programs correspond to the same input-output behavior. The upshot of yet another model of computation is that a categorical formalism should provide a…

In Formal Languages and Automata Theory courses, students find understanding nondeterministic finite-state and pushdown automata difficult. In many cases, this means that it is challenging for them to comprehend the operational semantics of…

Statecharts are frequently used as a modeling formalism in the design of state-based systems. Formal verification techniques are also often applied to prove certain properties about the behavior of the system. One of the most efficient…

A foundational question in quantum computational complexity asks how much more useful a quantum state can be in a given task than a comparable, classical string. Aaronson and Kuperberg showed such a separation in the presence of a quantum…

Simple spherical, non-rotating stellar models are inadequate when describing real stars in the limit of very fast rotation: Both the observable spectrum and the geometrical shape of the star deviate strongly from simple models. We attempt…

Asymmetric unification, or unification with irreducibility constraints, is a newly developed paradigm that arose out of the automated analysis of cryptographic protocols. However, there are still relatively few asymmetric unification…