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About 1,615 papers for “Halting problem”

Problem Halting Problem

Eric C. R. Hehner · 2014

Abstract Halting cannot be computed due to inconsistency of specification. The first proof that halting is incomputable was by Alan Turing in 1936 [1]. I begin by presenting Turing's proof, but modernized in two respects. Instead of using Turing Machine operations, I use a modern programming language: Pascal. To apply a function to the domain of programs, Turing encoded programs as numbers. Today, when one program is presented as input data to another program (for example, to a compiler or interpreter), it is represented as a text (character string), and that's the encoding I will use. These changes are standard in modern textbooks; they change nothing essential in the proof of incomputability. I cannot write a program to say whether the execution of any program halts, so instead I write the function header, and a comment to specify what the result of the function is supposed to be. Following the program is the standard argument leading to the incomputability conclusion. 0 function halts (p, i: string): boolean; { returns true if string p represents a procedure with one string input}

Cited by 0

Turing's Halting Problem Error

choi, ho yeol · Zenodo (CERN European Organization for Nuclear Research) · 2025

error of halting problem

Cited by 0Open access

Halting Problem Simulation in C

Olcott, P. · PhilPapers (PhilPapers Foundation)

The notion of a simulating termination analyzer can easily defeat the counter-example input of the halting problem because the contradictory part of this input becomes unreachable under simulation. Simulating termination analyzer HHH does correctly report the halt status that its input DD actually specifies.

Cited by 0

HALTING PROBLEM AND INCOMPLETENESS THEOREM

Yoriyuki Yamagata · 2012

Theorem 1. The following statements are equivalent, that is, we can prove each clause from the other clauses. (1) No sound, recursively axiomatizable arithmetic which contains Robinson Arithmetic Q can prove its own consistency. (Gödel’s second incompleteness

Cited by 0

The eight-minute halting problem

J. Paul Myers · ACM SIGCSE Bulletin · 1998

After years of presumed emphasis of CS theory in the curriculum, it is currently in vogue to downplay, if not disparage, a significant role for theoretical issues. This is being done with such vigor, however, that some are advocating an abandonment of even such topics as unsolvability as being no longer fundamental to a well-educated computing professional. An appeal is made, using the universal acknowledgment of the importance of the liberal arts to any well-educated person, to assert that certain theoretical topics are part of our liberal arts heritage. Moreover, students find even a brief presentation of these topics to be very illuminating.

Cited by 0Open access

Getting around the Halting Problem

X. Y. Newberry · arXiv (Cornell University) · 2017

There are numbers k and s and a URM program A(n,m) satisfying the following conditions. 1. If A(n,m) halts, then Cn(m) diverges. 2. For all n, C_k(n) = A(n,n) and C_s(n) = C_k(s). 3. A(k,s) halts and for all n, A(s,n) diverges. Here C_n(_) is a program with index n in some exhaustive enumeration of all possible programs. This has implications for solving the liar paradox and for generalization of Gödel incompleteness theorem to formal systems other than PA.

Cited by 0Open access

The Halting Problem is Incoherent

Olcott, P. · PhilPapers (PhilPapers Foundation)

Ever since 1997 the author has investigated the fundamental nature of “true on the basis of meaning”. The traditional analytic / synthetic distinction is unequivocally demarcated into: (a) True on the basis of meaning fully expressed as relations between finite strings. (b) True that can only be verified by sense data from the sense organs. Any system of reasoning that begins with a consistent set of stipulated truths and only applies the truth preserving operation of semantic logical entailment to this finite set of basic facts inherently derives a truth predicate that works consistently and correctly for this entire body of knowledge that can be expressed in language. “The halting problem, as classically formulated, relies on an inferential step that is not justified by a continuous chain of semantic entailment from its initial stipulations.”

Cited by 0

The Halting Problem Relativized to Complements

Louise Hay · Proceedings of the American Mathematical Society · 1973

Let ${H^A} = \{ e|{\text {domain}}\{ e\} \cap A \ne \emptyset \}$. It is shown that there exists a set $A$ of Turing degree $a$ such that ${H^A}$ is Turing-incomparable to ${H^{\bar A}}$ whenever $a$ is an r.e. degree with $a’ > 0’$, or $a \geqq 0''$ or $a \geqq 0’$ and $a$ is r.e. in 0’. This contrasts with the fact that ${H^A}$ is comparable to ${H^{\bar A}}$ for almost all $A$.

Cited by 4

EQUIVALENCE RELATIONS AND THE HALTING PROBLEM

Rodney Downey, Alexander G. Melnikov, Keng et al. · 2015

Abstract. We investigate which computable equivalence structures are isomorphic relative to the Halting problem. 1.

Cited by 0

0 Problems with the Halting Problem

Eric C. R. Hehner · 2011

Abstract Either we leave the definition of the halting function incomplete, not saying its result when applied to its own program, or we suffer inconsistency. If we choose incompleteness, we cannot require a halting program to apply to programs that invoke the halting program, and we cannot conclude that it is incomputable. If we choose inconsistency, then it makes no sense to propose a halting program. Either way, the incomputability argument is lost.

Cited by 0