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We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant…
String transductions that are definable in monadic second-order (mso) logic (without the use of parameters) are exactly those realized by deterministic two-way finite state transducers. Nondeterministic mso definable string transductions…
Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are…
This paper clarifies the picture about Dense-choice Counter Machines, which have been less studied than (discrete) Counter Machines. We revisit the definition of "Dense Counter Machines" so that it now extends (discrete) Counter Machines,…
Transformers have demonstrated remarkable performance in natural language processing and related domains, as they largely focus on sequential, autoregressive next-token prediction tasks. Yet, they struggle in logical reasoning, not…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can…
Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has…
Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for…
The Wyner-Ahlswede-K\"orner (WAK) empirical-coordination problem where the encoders cooperate via a finite-capacity one-sided link is considered. The coordination-capacity region is derived by combining several source coding techniques,…
In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…
Exponential error bounds achievable by universal coding and decoding are derived for frame-asynchronous discrete memoryless %asynchronous multiple access channels with two senders, via the method of subtypes, a refinement of the method of…
A two-dimensional finite automaton has a read-only input head that moves in four directions on a finite array of cells labelled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves,…
We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…
Despite their central role in the success of foundational models and large-scale language modeling, the theoretical foundations governing the operation of Transformers remain only partially understood. Contemporary research has largely…
We report on recent progress in understanding confinement of colour in $QCD$ as dual superconductivity of the vacuum. A gauge invariant version of the creation operator of monopoles is constructed whose vacuum expectation value is the order…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that…