Related papers: A Bisimulation-Invariance-Based Approach to the Se…
We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata…
This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
Partially ordered patterns (POPs) generalize the notion of classical patterns studied in the literature in the context of permutations, words, compositions and partitions. In this paper, we give a number of general, and specific enumerative…
We investigate the breaking of SU(3) into its subgroups from the viewpoints of explicit and spontaneous breaking. A one-to-one link between these two approaches is given by the complex spherical harmonics, which form a complete set of…
While theoretical computer science primarily works with discrete models of computation, like the Turing machine and the wordRAM, there are many scenarios in which introducing real computation models is more adequate. We want to compare real…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
The relationship between the complexity classes P and NP is a question that has not yet been answered by the Theory of Computation. The existence of a language in NP, proven not to belong to P, is sufficient evidence to establish the…
To a definable subset of Z_p^n (or to a scheme of finite type over Z_p) one can associate a tree in a natural way. It is known that the corresponding Poincare series P(X) = \sum_i N_i X^i is rational, where N_i is the number of nodes of the…
The causal graph of a planning instance is an important tool for planning both in practice and in theory. The theoretical studies of causal graphs have largely analysed the computational complexity of planning for instances where the causal…
We extend our previous work from arXiv:1903.06863 on biquandle module invariants of oriented surface-links to the case of unoriented surface-links using bikei modules. The resulting infinite family of enhanced invariants proves be effective…
In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for…
Let $X$ be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on $X$. For that purpose, we construct the virtual fundamental…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
We present bipartiteSUSY, a Mathematica package designed to perform calculations for physical theories based on bipartite graphs. In particular, the package can employ the recently developed arsenal of techniques surrounding on-shell…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods…
A perturbative expansion of knot invariants is derived using quantum cluster algebras. By interpreting the $R$-matrix of $U_q(\mathfrak{sl}_2)$ as a cluster transformation and introducing an auxiliary parameter $\epsilon$, we derive a…
Let $F$ be any field of characteristic $p$. It is well-known that there are exactly $p$ inequivalent indecomposable representations $V_1,V_2,...,V_p$ of $C_p$ defined over $F$. Thus if $V$ is any finite dimensional $C_p$-representation…