From results of Ishihara it is known that the weak (that is, binary) form of König’s lemma (WKL) implies Brouwer’s fan theorem (Fan). Moreover, Berger and Ishihara [MLQ 2005] have shown that a weakened form WKL! of WKL, where as an additional hypothesis it is required that in an effective sense infinite paths are unique, is equivalent to Fan. The proof that WKL! implies Fan is done explicitely....

We compare two proofs of the mutual-exclusion property of the well known critical section algorithm of Peterson: an assertional proof and a behavioral one. The accepted view is that behavioral proofs are informal and are, for some intrinsic reason, error prone. We try to present a different view and to outline a framework within which the behavioral approach can be formalized in a way that keep...

In past years, a l q g e number of published distributed algorithms have been shown to be incorrect. Unfortunately, designers of distributed algorithms typically use informal correctness proofs, which tend to be unreliable. Formal correctness proofs offer a much higher degree of reliability, but they are not popular among algorithm designers because they are too mathematical and they typically ...

In this work, we propose a variant of P system based on the rewriting of string-objects by means of evolutionary rules. The membrane structure of such a P system seems to be a very natural tool for simulating the filters in accepting networks of evolutionary processors with filtered connections. We discuss an informal construction supporting this simulation. A detailed proof is to be considered...

In this work, we propose a variant of P system based on the rewriting of string-objects by means of evolutionary rules. The membrane structure of such a P system seems to be a very natural tool for simulating the filters in accepting networks of evolutionary processors with filtered connections. We discuss an informal construction supporting this simulation. A detailed proof is to be considered...

This paper presents an approach to formalize COM. Despite its importance, COM still does not have a formal speciication. In order to understand the COM's informal rules better, the COMEL language is being introduced. We formalized some of the important COM's rules and present COMEL's abstract syntax and type system. Work is still progressing on the operational semantics of COMEL and the soundne...

In this paper we present a recursive implementation of the Agrawal, Kayal and Saxena primality testing algorithm, which is the first unconditional deterministic polynomial time primality testing algorithm. Since the algorithm’s proof of correctness makes use of informal notation and omits many key steps, we present the progress made toward using ACL2 to verify the algorithm’s correctness. In pa...

Symbolic execution is a program verification technique born in the 1970s. One of the first papers in the area by King [5] describes the technique as being somewhere between the informal and the formal approaches. The informal approach may be described as follows: the developer creates test cases which are sets of input values to be provided to the application; these test cases are ran against t...

Introduction Informal patient payments for healthcare are common in the Western Balkans, negatively affecting public health and healthcare.   Aim To identify literature from the Western Balkans on what is known about informal patient payments and bought and brought goods, to examine their effects on healthcare and to determine what actions can be taken to tackle these payments.   Methods After ...