Related papers: Computational Power of P Systems with Small Size I…

Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…

Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…

Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…

The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to…

The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…

Can purely mechanical systems generate intelligent language? We prove that dissipative quantum dynamics with analytically tractable non-local context aggregation produce coherent text generation, while conservation laws cause fundamental…

Much recent work has shown how cross-linguistic variation is constrained by competing pressures from efficient communication. However, little attention has been paid to the role of the systematicity of forms (regularity), a key property of…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same…

We consider P systems with a linear membrane structure working on objects over a unary alphabet using sets of rules resembling homomorphisms. Such a restricted variant of P systems allows for a unique minimal representation of the generated…

Clausal Language (CL) is a declarative programming and verifying system used in our teaching of computer science. CL is an implementation of, what we call, $\mathit{PR}{+}I\Sigma_1$ paradigm (primitive recursive functions with…

Whenever P is a proper definable forcing for adding a real, the countable support iteration of P has all the preservation properties it can possibly have, within a wide syntactically identified class of properties.

A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…

LS is a particular type of computational processes simulating living tissue. They use an unlimited branching process arising from the simultaneous substitutions of some words instead of letters in some initial word. This combines the…

We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enumerable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for…

Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…

In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…

Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…

We present a new method for large language models to solve compositional tasks. Although they have shown strong performance on traditional language understanding tasks, large language models struggle to solve compositional tasks, where the…