Related papers: Reactive Turing Machines with Infinite Alphabets
For computation, there existed Turing machine and later-matured automata theory. For low-level parallel computation, there existed variants of Turing machine, such as two-tapes Turing machine and multi-tapes Turing machine. In the…
Traditional Turing machines are semantically poor, they only concern the syntactic manipulation of symbols, discarding the mathematical semantics behind the symbols. This semantic deficiency is considered the root cause of the three major…
Context: Reactive programming (RP) is a declarative programming paradigm suitable for expressing the handling of events. It enables programmers to create applications that react automatically to changes over time. Whenever a time-varying…
Refinement calculus is a powerful and expressive tool for reasoning about sequential programs in a compositional manner. In this paper we present an extension of refinement calculus for reactive systems. Refinement calculus is based on…
The Neural Turing Machine (NTM) is more expressive than all previously considered models because of its external memory. It can be viewed as a broader effort to use abstract external Interfaces and to learn a parametric model that interacts…
In this paper, we show that, under mild assumptions, input-output behavior of a continous-time recurrent neural network (RNN) can be represented by a rational or polynomial nonlinear system. The assumptions concern the activation function…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
Due to the limitation on computational power of existing computers, the polynomial time does not works for identifying the tractable problems in big data computing. This paper adopts the sublinear time as the new tractable standard to…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
So far, following the works of A.M. Turing, the algorithms were considered as the mathematical abstraction from which we could write programs for computers whose principle was based on the theoretical concept of Turing machine. We start…
Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the…
The Turing machine (TM) and the Church thesis have formalized the concept of computable number, this allowed to display non-computable numbers. This paper defines the concept of number "approachable" by a TM and shows that some (if not all)…
Computational complexity characterizes the usage of spatial and temporal resources by computational processes. In the classical theory of computation, e.g. in the Turing Machine model, computational processes employ only local space and…
It is a great pleasure to write this tribute in honor of Scott A. Smolka on his 65th birthday. We revisit Goldin, Smolka hypothesis that persistent Turing machine (PTM) can capture the intuitive notion of sequential interaction computation.…
Neural reasoners such as Tiny Recursive Models (TRMs) solve complex problems by combining neural backbones with specialized inference schemes. Such inference schemes have been a central component of stochastic reasoning systems, where…
Reversible computation is an unconventional form of computing where any executed sequence of operations can be executed in reverse at any point during computation. It has recently been attracting increasing attention in various research…
A fundamental question is whether Turing machines can model all reasoning processes. We introduce an existence principle stating that the perception of the physical existence of any Turing program can serve as a physical causation for the…
To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a…
Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…