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Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
We show how entanglement can be used, without being consumed, to accomplish unitary operations that could not be performed with out it. When applied to infinitesimal transformations our method makes equivalent, in the sense of Hamiltonian…
Card-based cryptography is a research area to implement cryptographic procedures using a deck of physical cards. In recent years, it has been found to be related to finite group theory and algebraic combinatorics, and is becoming more and…
Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term…
In this paper we propose a calculus for expressing algorithms for programming languages transformations. We present the type system and operational semantics of the calculus, and we prove that it is type sound. We have implemented our…
Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In…
Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about…
We show that induction of covariant representations for C*-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of…
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
We shall characterize the structure of invertible substitutions on three-letter alphabet. We show that any invertible substitution, after some cyclic operation, can be written as a finite product of permutations and Fibonacci's…
Let I be an arbitrary ideal in C[[x,y]]. We use the Newton algorithm to compute by induction the motivic zeta function of the ideal, yielding only few poles, associated to the faces of the successive Newton polygons. We associate a minimal…
Deep learning often faces the challenge of efficiently processing dynamic inputs, such as sensor data or user inputs. For example, an AI writing assistant is required to update its suggestions in real time as a document is edited.…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
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…
The entanglement theory in quantum systems with internal symmetries is rich due to the spontaneous creation of entangled pairs of charge/anti-charge particles at the entangling surface. We call these pair creation operators the bi-local…
Quantum language models have shown competitive performance on sequential tasks, yet whether trained quantum circuits exploit genuinely quantum resources -- or merely embed classical computation in quantum hardware -- remains unknown. Prior…
We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…
We introduce notions of simulation between semiring-weighted automata as models of quantitative systems. Our simulations are instances of the categorical/coalgebraic notions previously studied by Hasuo---hence soundness against language…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…