相关论文: Well-founded Iterations of Infinite Time Turing Ma…

This paper is the extended version of On the Complexity of Infinite Advice Strings (ICALP 2018). We investigate a notion of comparison between infinite strings. In a general way, if M is a computation model (e.g. Turing machines) and C a…

Turing Machines are universal computing machines in theory. It has been a long debate whether Turing Machines can simulate the consciousness mind behaviors in the materialistic universe. Three different hypotheses come out of such debate,…

We study the question of what is computable by Turing machines equipped with time travel into the past; i.e., with Deutschian closed timelike curves (CTCs) having no bound on their width or length. An alternative viewpoint is that we study…

Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a…

The article contains an outline of a possible new direction for Computability Logic (see www.csc.villanova.edu/~japaridz/CL/ ), focused on computability without infinite memory or other impossible-to-possess computational resources. The new…

The strong, intermediate, and weak Turing impossibility properties are introduced. Some facts concerning Turing impossibility for stack machine programming are trivially adapted from previous work. Several intriguing questions are raised…

Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…

We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…

The paper presents an extension of temporal epistemic logic with operators that quantify over strategies. The language also provides a natural way to represent what agents would know were they to be aware of the strategies being used by…

We consider computations of a Turing machine subjected to noise. In every step, the action (the new state and the new content of the observed cell, the direction of the head movement) can differ from that prescribed by the transition…

As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring such questions can help…

We consider the computational model of the Queue Automaton. An old result is that the deterministic queue automaton is equally expressive as the Turing machine. We introduced the Reactive Turing Machine, enhancing the Turing machine with a…

Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…

Interrupt Timed Automata (ITA) is an expressive timed model, introduced to take into account interruptions, according to levels. Due to this feature, this formalism is incomparable with Timed Automata. However several decidability results…

P systems are computing conceptual computing devices that are at least as powerful as Turing machines. However, until recently it was not known how one can encode any recursive function as a P~system. Here we propose a new encoding of…

At a first glance the Theory of computation relies on potential infinity and an organization aimed at solving a problem. Under such aspect it is like Mendeleev theory of chemistry. Also its theoretical development reiterates that of this…

We show that transformer-based large language models are computationally universal when augmented with an external memory. Any deterministic language model that conditions on strings of bounded length is equivalent to a finite automaton,…

Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signalling an end of a calculation by setting a halt…

A concept of randomness for infinite time register machines (ITRMs) is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies computability and that an analogue of…

We clarify the confusion, misunderstanding and misconception that the physical finiteness of the universe, if the universe is indeed finite, would rule out all hypercomputation, the kind of computation that exceeds the Turing computability,…