相关论文: Representing a P-complete problem by small trellis…
The class of known constraint automata for which the constrained synchronization problem is in NP all admit a special form. In this work, we take a closer look at them. We characterize a wider class of constraint automata that give…
Solving arithmetic word problems is a cornerstone task in assessing language understanding and reasoning capabilities in NLP systems. Recent works use automatic extraction and ranking of candidate solution equations providing the answer to…
Sentence completion (SC) questions present a sentence with one or more blanks that need to be filled in, three to five possible words or phrases as options. SC questions are widely used for students learning English as a Second Language…
We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the…
Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring…
The value 1 problem is a decision problem for probabilistic automata over finite words: are there words accepted by the automaton with arbitrarily high probability? Although undecidable, this problem attracted a lot of attention over the…
A finitary automaton group is a group generated by an invertible, deterministic finite-state letter-to-letter transducer whose only cycles are self-loops at an identity state. We show that, for this presentation of finite groups, the…
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…
A Boolean network is a discrete dynamical system operating on vectors of Boolean variables. The action of a Boolean network can be conveniently expressed as a system of Boolean update functions, computing the new values for each component…
For many cellular automata, it is possible to express the state of a given cell after $n$ iterations as an explicit function of the initial configuration. We say that for such rules the solution of the initial value problem can be obtained.…
This paper presents a new genetic algorithm encoding representation to solve the travelling salesman problem. To assess the performance of the proposed chromosome structure, we compare it with state-of-the-art encoding representations. For…
A word is called a reset word for a deterministic finite automaton if it maps all the states of the automaton to a unique state. Deciding about the existence of a reset word of a given maximum length for a given automaton is known to be an…
It is already shown that a Boolean function for a NP-complete problem can be computed by a polynomial-sized circuit if its variables have enough number of automorphisms. Looking at this previous study from the different perspective gives us…
We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…
In this paper we summarize the existing principles for building unconventional computing devices that involve delayed signals for encoding solutions to NP-complete problems. We are interested in the following aspects: the properties of the…
In this report, we describe three encodings of the multiple constant multiplication (MCM) problem to pseudo-boolean satisfiability (PBS), and introduce an algorithm to solve the MCM problem optimally. To the best of our knowledge, the…
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to non-zero probability transitions in single…
A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open…
A necessary and sufficient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two different forms of simpler and more visual representations of these rules are given, and their…