Related papers: Kleene Theorem for Higher-Dimensional Automata
We propose a new extension of higher-order pushdown automata, which allows to use an infinite alphabet. The new automata recognize languages of data words (instead of normal words), which beside each its letter from a finite alphabet have a…
In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the…
The operator precedence languages (OPLs) represent the largest known subclass of the context-free languages which enjoys all desirable closure and decidability properties. This includes the decidability of language inclusion, which is the…
Machine learning has gained widespread attention as a powerful tool to identify structure in complex, high-dimensional data. However, these techniques are ostensibly inapplicable for experimental systems where data is scarce or expensive to…
We show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter…
Recent work on tokenizer-free multilingual pretrained models show promising results in improving cross-lingual transfer and reducing engineering overhead (Clark et al., 2022; Xue et al., 2022). However, these works mainly focus on reporting…
The use of Extended Logics to replace ordinary second order definability in Kleene's {\em Ramified Analytical Hierarchy} is investigated. This mirrors a similar investigation of Kennedy, Magidor and V\"a\"an\"anen \cite{KeMaVa2016} where…
We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…
We introduce a novel automata model, called pebble-intervals automata (PIA), and study its power and closure properties. PIAs are tailored for a decidable fragment of FO that is important for reasoning about structures that use data values…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
Kleene algebra with tests (KAT) is a foundational equational framework for reasoning about programs, which has found applications in program transformations, networking and compiler optimizations, among many other areas. In his seminal…
Reaction automata are a formal model that has been introduced to investigate the computing powers of interactive behaviors of biochemical reactions([14]). Reaction automata are language acceptors with multiset rewriting mechanism whose…
We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore,…
Debiased machine learning (DML) offers an attractive way to estimate treatment effects in observational settings, where identification of causal parameters requires a conditional independence or unconfoundedness assumption, since it allows…
Prompt engineering has emerged as a powerful technique for guiding large language models (LLMs) toward desired responses, significantly enhancing their performance across diverse tasks. Beyond their role as static predictors, LLMs…
We exhibit a uniform method for obtaining (wellfounded and non-wellfounded) cut-free sequent-style proof systems that are sound and complete for various classes of action algebras, i.e., Kleene algebras enriched with meets and residuals.…
Commonsense reasoning has long been considered as one of the holy grails of artificial intelligence. Most of the recent progress in the field has been achieved by novel machine learning algorithms for natural language processing. However,…
Large, pretrained language models infer powerful representations that encode rich semantic and syntactic content, albeit implicitly. In this work we introduce a novel neural language model that enforces, via inductive biases, explicit…
In the literature on Kleene algebra, a number of variants have been proposed which impose additional structure specified by a theory, such as Kleene algebra with tests (KAT) and the recent Kleene algebra with observations (KAO), or make…
We study subsystems of open induction which are strongly connected to methods of automated inductive theorem proving. Specifically, we consider systems obtained from restricting induction to atoms, literals, clauses, and dual clauses. We…