Related papers: Regular resynchronizability of origin transducers …
Analogy is a central faculty of human intelligence, enabling abstract patterns discovered in one domain to be applied to another. Despite its central role in cognition, the mechanisms by which Transformers acquire and implement analogical…
We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between $M$ quantum states that become identical under a completely decohering map. Similarly, we study distinguishability…
Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…
In this first part, a computable outer bound is proved for the multiterminal source coding problem, for a setup with two encoders, discrete memoryless sources, and bounded distortion measures.
In this technical note, we study the problem of inverse permutation learning in decoder-only transformers. Given a permutation and a string to which that permutation has been applied, the model is tasked with producing the original…
For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior…
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…
The purpose of this paper is to present an algorithm for inferring nondeterministic functional transducers. It has a lot in common with other well known algorithms such has RPNI and OSTIA. Indeed we will argue that this algorithm is a…
We prove that the pattern matching problem is undecidable in polymorphic lambda-calculi (as Girard's system F) and calculi supporting inductive types (as G{\"o}del's system T) by reducing Hilbert's tenth problem to it. More generally…
"Unidirectional channel systems" (Chambart & Schnoebelen, CONCUR 2008) are finite-state systems where one-way communication from a Sender to a Receiver goes via one reliable and one unreliable unbounded fifo channel. While reachability is…
Recent theoretical models of diffusion processes, conceptualized as coupled Ornstein-Uhlenbeck systems, predict a hierarchy of interaction timescales, and consequently, the existence of a synchronization gap between modes that commit at…
Transformers process tokens in parallel but are temporally shallow: at position $t$, each layer attends to key-value pairs computed based on the previous layer, yielding a depth capped by the number of layers. Recurrent models offer…
We position Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines. The mere requirement that a program of a certain kind must solve the halting problem for all programs of that…
In rule-based systems, goal-oriented computations correspond naturally to the possible ways that an observation may be explained. In some applications, we need to compute explanations for a series of observations with the same domain. The…
Distinguishability is a fundamental and operational task generally connected to information applications. In quantum information theory, from the postulates of quantum mechanics it often has an intrinsic limitation, which then dictates and…
Classic distributed control problems have an interesting dichotomy: they are either trivial or undecidable. If we allow the controllers to fully synchronize, then synthesis is trivial. In this case, controllers can effectively act as a…
The relation between nonanticipative Rate Distortion Function (RDF) and filtering theory is discussed on abstract spaces. The relation is established by imposing a realizability constraint on the reconstruction conditional distribution of…
We show that conjugacy of reversible cellular automata is undecidable, whether the conjugacy is to be performed by another reversible cellular automaton or by a general homeomorphism. This gives rise to a new family of finitely-generated…
We consider input-deterministic finite state transducers with infinite inputs and infinite outputs, and we consider the property of Borel normality on infinite words. When these transducers are given by a strongly connected set of states,…
In this paper we study the order parameter and density of states near a grain boundary between two $d_{x^2-y^2}$ superconductors. We examine broken time reversal symmetry near the interface. In particular we show that, under suitable…