Related papers: Visualizing a Nondeterministic to Deterministic Fi…
The main goal of this paper is to give a rigorous mathematical description of systems for processing quantum information. To do it authors consider abstract state machines as models of classical computational systems. This class of machines…
Finite-state automata are a very effective tool in natural language processing. However, in a variety of applications and especially in speech precessing, it is necessary to consider more general machines in which arcs are assigned weights…
Finite state machines (FSMs) are widely used to manage robot behavior logic, particularly in real-world applications that require a high degree of reliability and structure. However, traditional manual FSM design and modification processes…
Despite recent progress in artificial intelligence and machine learning, many state-of-the-art methods suffer from a lack of explainability and transparency. The ability to interpret the predictions made by machine learning models and…
As the intermediate-level representations bridging the two levels, structured representations of visual scenes, such as visual relationships between pairwise objects, have been shown to not only benefit compositional models in learning to…
Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
Nondeterministic Discounted-Sum Automata (NDAs) are nondeterministic finite automata equipped with a discounting factor $\lambda>1$, and whose transitions are labelled by weights. The value of a run of an NDA is the discounted sum of the…
We consider ways to construct a transducer for a given set of input word to output symbol pairs. This is motivated by the need for representing game playing programs in a low-level mathematical format that can be analyzed by algebraic…
Soliton automata are mathematical models of soliton switching in chemical molecules. Several concepts of determinism for soliton automata have been defined. The concept of strong determinism has been investigated for the case in which only…
Finite state machines are widely used as a sound mathematical formalism that appropriately describes large scale, distributed and complex systems. Multiple interactions of finite state machines in complex systems are well captured by the…
We define a language-independent model of nondeterministic quantum programs in which a quantum program consists of a finite set of quantum processes. These processes are represented by quantum Markov chains over the common state space. An…
Intuitively, an (implementation) automata is simulated by a (specification) automata if every externally observable transition by the implementation automata can also be made by the specification automata. In this work, we present a…
Finite-state abstractions (a.k.a. symbolic models) present a promising avenue for the formal verification and synthesis of controllers in continuous-space control systems. These abstractions provide simplified models that capture the…
We characterize complete deterministic finite automata with two input letters in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word. The characterization leads to a…
We consider the previously defined notion of finite-state independence and we focus specifically on normal words. We characterize finite-state independence of normal words in three different ways, using three different kinds of asynchronous…
While many applications of automata in formal methods can use nondeterministic automata, some applications, most notably synthesis, need deterministic or good-for-games (GFG) automata. The latter are nondeterministic automata that can…
Any two-way finite state automaton is equivalent to some one-way finite state automaton. This well-known result, shown by Rabin and Scott and independently by Shepherdson, states that two-way finite state automata (even non-deterministic)…
Hereditarily finite (HF) set theory provides a standard universe of sets, but with no infinite sets. Its utility is demonstrated through a formalisation of the theory of regular languages and finite automata, including the Myhill-Nerode…
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these…