In this work the handover in a Bluetooth scatternet is studied. The procedure of inquiry defined by the Bluetooth standard to create and manage an adhoc network could be used also to perform the handover but is too slow to keep the communication active. Here a procedure on-demand, based on an accurate paging, is proposed. The parameters needed to perform the handover are exchanged when necessar...

Deductive synthesis methods derive programs in an incremental manner, and therefore pose a halting problem { when can synthesis stop with a correct program? We give a characterisation of this problem and state a halting principle as a solution. Another characteristic of deductive synthesis is that it may derive several correct programs, giving rise to another question { which correct programs a...

We give a new proof for the decidability of the binary Post Correspondence Problem (PCP) originally proved in 1982 by Ehrenfeucht, Karhum8 aki and Rozenberg. Our proof is complete and somewhat shorter than the original proof although we use the same basic idea. c © 2002 Elsevier Science B.V. All rights reserved.

Is there any hope for quantum computing to challenge the Turing barrier, i.e. to solve an undecidable problem, to compute an uncomputable function? According to Feynman’s ’82 argument, the answer is negative. This paper re-opens the case: we will discuss solutions to a few simple problems which suggest that quantum computing is theoretically capable of computing uncomputable functions. Turing p...

A problem/conjecture is finitely refutable if verifying a finite number of instances suffices to disprove it. A systematic enumeration (of the problem’s search domain) will find a counter-example if one exists. If the search stops, the conjecture is false; if the search does not halt the conjecture is true. For a finitely refutable problem Π we can construct a program CΠ such that Π is false if...

What is the meaning of hypercomputation, the meaning of computing more than the Turing machine? Concrete non-computable functions always hide the halting problem as far as we know. Even the construction of a function that grows faster than any recursive function — the Busy Beaver — a more natural function, hides the halting function, that can easily be put in relation with the Busy Beaver. Is t...

We formally verify several computational reductions concerning the Post correspondence problem (PCP) using the proof assistant Coq. Our verifications include a reduction of a string rewriting problem generalising the halting problem for Turingmachines to PCP, and reductions of PCP to the intersection problem and the palindrome problem for context-free grammars. A rigorous correctness proof for ...

Concrete non-computable functions are usually related to the halting function. Is it possible to present examples of non-computability, which are unrelated to the halting problem and its derivatives? We built an abstract machine based on the historic concept of compass and ruler constructions (a compass construction would suffice) which reveals the existence of non-computable functions not rela...