Related papers: How Concise are Chains of co-B\"uchi Automata?
Recent advancements in Chain-of-Thought (CoT) reasoning utilize complex modules but are hampered by high token consumption, limited applicability, and challenges in reproducibility. This paper conducts a critical evaluation of CoT…
In this work we introduce a deterministic scheme of synchronization of linear and nonlinear cellular automata (CA) with complex behavior, connected through a master-slave coupling. By using a definition of Boolean derivative, we use the…
The states of a deterministic finite automaton A can be identified with collections of words in Pf(L(A)) -- the set of prefixes of words belonging to the regular language accepted by A. But words can be ordered and among the many possible…
Families of deterministic finite automata (FDFA) represent regular $\omega$-languages through their ultimately periodic words (UP-words). An FDFA accepts pairs of words, where the first component corresponds to a prefix of the UP-word, and…
This work considers weak deterministic B\"uchi automata reading encodings of non-negative $d$-vectors of reals in a fixed base. A saturated language is a language which contains all encoding of elements belonging to a set of $d$-vectors of…
We consider ideals and Boolean combinations of ideals. For the regular languages within these classes we give expressively complete automaton models. In addition, we consider general properties of regular ideals and their Boolean…
The determinization of a nondeterministic B\"uchi automaton (NBA) is a fundamental construction of automata theory, with applications to probabilistic verification and reactive synthesis. The standard determinization constructions, such as…
We present a polynomial time algorithm that constructs a deterministic parity automaton (DPA) from a given set of positive and negative ultimately periodic example words. We show that this algorithm is complete for the class of…
We present Chain-of-Action (CoA), a novel visuo-motor policy paradigm built upon Trajectory Autoregressive Modeling. Unlike conventional approaches that predict next step action(s) forward, CoA generates an entire trajectory by explicit…
Many natural language processing systems operate over tokenizations of text to address the open-vocabulary problem. In this paper, we give and analyze an algorithm for the efficient construction of deterministic finite automata (DFA)…
We introduce a new family of neural network models called Convolutional Dynamic Alignment Networks (CoDA Nets), which are performant classifiers with a high degree of inherent interpretability. Their core building blocks are Dynamic…
Distributed optimization algorithms are essential for training machine learning models on very large-scale datasets. However, they often suffer from communication bottlenecks. Confronting this issue, a communication-efficient primal-dual…
We prove that two-way probabilistic and quantum finite automata (2PFA's and 2QFA's) can be considerably more concise than both their one-way versions (1PFA's and 1QFA's), and two-way nondeterministic finite automata (2NFA's). For this…
Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature. In the case of nondeterministic finite automata on finite words (NFA),…
The proliferation of agentic systems has thrust the reasoning capabilities of AI into the forefront of contemporary machine learning. While it is known that there \emph{exist} neural networks which can reason through any Boolean task…
Complementation of nondeterministic B\"uchi automata (BAs) is an important problem in automata theory with numerous applications in formal verification, such as termination analysis of programs, model checking, or in decision procedures of…
We introduce a new family of neural network models called Convolutional Dynamic Alignment Networks (CoDA-Nets), which are performant classifiers with a high degree of inherent interpretability. Their core building blocks are Dynamic…
The determinization of Buchi automata is a celebrated problem, with applications in synthesis, probabilistic verification, and multi-agent systems. Since the 1960s, there has been a steady progress of constructions: by McNaughton, Safra,…
Active automata learning infers automaton models of systems from behavioral observations, a technique successfully applied to a wide range of domains. Compositional approaches have recently emerged to address scalability to concurrent…
In this paper we define a new descriptional complexity measure for Deterministic Finite Automata, BC-complexity, as an alternative to the state complexity. We prove that for two DFAs with the same number of states BC-complexity can differ…