Asymptotic Proportion of Hard Instances of the Halting Problem

Asymptotic Proportion of Hard Instances of the Halting Problem

Although the halting problem is undecidable, imperfect testers that fail on some instances are possible. Such instances are called hard for the tester. One variant of imperfect testers replies “I don’t know” on hard instances, another variant fails to halt, and yet another replies incorrectly “yes” or “no”. Also the halting problem has three variants. A tester may test halting on the empty inpu...

The Asymptotic Behaviour of the Proportion of Hard Instances of the Halting Problem (Extended Version)

the problem of divine hiddenness

این رساله به مساله احتجاب الهی و مشکلات برهان مبتنی بر این مساله میپردازد. مساله احتجاب الهی مساله ای به قدمت ادیان است که به طور خاصی در مورد ادیان ابراهیمی اهمیت پیدا میکند. در ادیان ابراهیمی با توجه به تعالی خداوند و در عین حال خالقیت و حضور او و سخن گفتن و ارتباط شهودی او با بعضی از انسانهای ساکن زمین مساله ای پدید میاید با پرسشهایی از قبیل اینکه چرا ارتباط مستقیم ویا حداقل ارتباط وافی به ب...

Finding Hard Instances of the Satisfiability Problem

Finding sets of hard instances of propositional satissability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the ...

Autosolvability of halting problem instances for instruction sequences

We position Turing’s result regarding the undecidability of the halting problem as a result about programs rather than machines. The mere requirement that a program of a certain kind must solve the halting problem for all programs of that kind leads to a contradiction in the case of a recent unsolvability result regarding the halting problem for programs. In this paper, we investigate this auto...