4,862 research outputs found
Quasi-Delay-Insensitive Circuits are Turing-Complete
Quasi-delay-insensitive (QDI) circuits are those whose correct operation does not depend on the delays of operators or wires, except for certain wires that form isochronic forks. In this paper we show that quasi-delay-insensitivity, stability and noninterference, and strong confluence are equivalent properties of a computation. In particular, this shows that QDI computations are deterministic. We show that the class of Turing-computable functions have QDI implementations by constructing a QDI Turing machine
Problem Theory
The Turing machine, as it was presented by Turing himself, models the
calculations done by a person. This means that we can compute whatever any
Turing machine can compute, and therefore we are Turing complete. The question
addressed here is why, Why are we Turing complete? Being Turing complete also
means that somehow our brain implements the function that a universal Turing
machine implements. The point is that evolution achieved Turing completeness,
and then the explanation should be evolutionary, but our explanation is
mathematical. The trick is to introduce a mathematical theory of problems,
under the basic assumption that solving more problems provides more survival
opportunities. So we build a problem theory by fusing set and computing
theories. Then we construct a series of resolvers, where each resolver is
defined by its computing capacity, that exhibits the following property: all
problems solved by a resolver are also solved by the next resolver in the
series if certain condition is satisfied. The last of the conditions is to be
Turing complete. This series defines a resolvers hierarchy that could be seen
as a framework for the evolution of cognition. Then the answer to our question
would be: to solve most problems. By the way, the problem theory defines
adaptation, perception, and learning, and it shows that there are just three
ways to resolve any problem: routine, trial, and analogy. And, most
importantly, this theory demonstrates how problems can be used to found
mathematics and computing on biology.Comment: 43 page
Catalytic and communicating Petri nets are Turing complete
In most studies about the expressiveness of Petri nets, the focus has been put either on adding suitable arcs or on assuring that a complete snapshot of the system can be obtained. While the former still complies with the intuition on Petri nets, the second is somehow an orthogonal approach, as Petri nets are distributed in nature. Here, inspired by membrane computing, we study some classes of Petri nets where the distribution is partially kept and which are still Turing complete
Some Turing-Complete Extensions of First-Order Logic
We introduce a natural Turing-complete extension of first-order logic FO. The
extension adds two novel features to FO. The first one of these is the capacity
to add new points to models and new tuples to relations. The second one is the
possibility of recursive looping when a formula is evaluated using a semantic
game. We first define a game-theoretic semantics for the logic and then prove
that the expressive power of the logic corresponds in a canonical way to the
recognition capacity of Turing machines. Finally, we show how to incorporate
generalized quantifiers into the logic and argue for a highly natural
connection between oracles and generalized quantifiers.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Random strings and tt-degrees of Turing complete C.E. sets
We investigate the truth-table degrees of (co-)c.e.\ sets, in particular,
sets of random strings. It is known that the set of random strings with respect
to any universal prefix-free machine is Turing complete, but that truth-table
completeness depends on the choice of universal machine. We show that for such
sets of random strings, any finite set of their truth-table degrees do not meet
to the degree~0, even within the c.e. truth-table degrees, but when taking the
meet over all such truth-table degrees, the infinite meet is indeed~0. The
latter result proves a conjecture of Allender, Friedman and Gasarch. We also
show that there are two Turing complete c.e. sets whose truth-table degrees
form a minimal pair.Comment: 25 page
Java Generics are Turing Complete
This paper describes a reduction from the halting problem of Turing machines to subtype checking in Java. It follows that subtype checking in Java is undecidable, which answers a question posed by Kennedy and Pierce in 2007. It also follows that Java's type checker can recognize any recursive language, which improves a result of Gill and Levy from 2016. The latter point is illustrated by a parser generator for fluent interfaces
Turing Completeness of Finite, Epistemic Programs
In this note, we show the class of finite, epistemic programs to be Turing
complete. Epistemic programs is a widely used update mechanism used in
epistemic logic, where it such are a special type of action models: One which
does not contain postconditions
Sleptsov Nets are Turing-complete
The present paper proves that a Sleptsov net (SN) is Turing-complete, that
considerably improves, with a brief construct, the previous result that a
strong SN is Turing-complete. Remind that, unlike Petri nets, an SN always
fires enabled transitions at their maximal firing multiplicity, as a single
step, leaving for a nondeterministic choice of which fireable transitions to
fire. A strong SN restricts nondeterministic choice to firing only the
transitions having the highest firing multiplicity.Comment: Sleptsov Net Computing Resolves Modern Supercomputing Problems,
https://technews.acm.org/archives.cfm?fo=2023-04-apr/apr-21-2023.htm
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