Generic algorithms for halting problem and optimal machines revisited

Generic algorithms for halting problem and optimal machines revisited

A classical result says that the halting problem is undecidable: there is no algorithm that, given a computation, says whether it terminates or not. A related result says that for some computations the termination statement is undecidable in Gödel’s sense (neither provable nor refutable). Still in many cases the termination question is not that hard. Maybe, the difficult cases are rare exceptio...

On the strongly generic undecidability of the Halting Problem

Optimal Placement Algorithms for Virtual Machines

Cloud computing provides a computing platform for the users to meet their demands in an efficient, cost-effective way. Virtualization technologies are used in the clouds to aid the efficient usage of hardware. Virtual machines (VMs) are utilized to satisfy the user needs and are placed on physical machines (PMs) of the cloud for effective usage of hardware resources and electricity in the cloud...

Generic algorithms for the discrete logarithm problem

This can be a significantly harder problem. For example, say we are using a randomized (Las Vegas) algorithm. If β lies in 〈α〉 then we are guaranteed to eventually find logα β, but if not, we will never find it and it may be impossible to tell whether we are just very unlucky or β 6∈ 〈α〉. On the other hand, with a deterministic algorithm such as the baby-steps giant-steps method, we can unequiv...

A Parameterized Halting Problem

The parameterized problem p-Halt takes as input a nondeterministic Turing machine M and a natural number n, the size of M being the parameter. It asks whether every accepting run of M on empty input tape takes more than n steps. This problem is in the class XPuni, the class “uniform XP,” if there is an algorithm deciding it, which for fixed machine M runs in time polynomial in n. It turns out t...