Computational Processes and Incompleteness

We introduce a formal definition of Wolfram's notion of computational process based on cellular automata, a physics-like model of computation. There is a natural classification of these processes into decidable, intermediate and complete. It is shown that in the context of standard finite injury priority arguments one cannot establish the existence of an intermediate computational process

Random strings and tt-degrees of Turing complete C.E. sets

We investigate the truth-table degrees of (co-)c.e.\ sets, in particular, sets of random strings. It is known that the set of random strings with respect to any universal prefix-free machine is Turing complete, but that truth-table completeness depends on the choice of universal machine. We show that for such sets of random strings, any finite set of their truth-table degrees do not meet to the degree~0, even within the c.e. truth-table degrees, but when taking the meet over all such truth-table degrees, the infinite meet is indeed~0. The latter result proves a conjecture of Allender, Friedman and Gasarch. We also show that there are two Turing complete c.e. sets whose truth-table degrees form a minimal pair.Comment: 25 page

Ramsey-type graph coloring and diagonal non-computability

A function is diagonally non-computable (d.n.c.) if it diagonalizes against the universal partial computable function. D.n.c. functions play a central role in algorithmic randomness and reverse mathematics. Flood and Towsner asked for which functions h, the principle stating the existence of an h-bounded d.n.c. function (DNR_h) implies the Ramsey-type K\"onig's lemma (RWKL). In this paper, we prove that for every computable order h, there exists an~$\omega$-model of DNR_h which is not a not model of the Ramsey-type graph coloring principle for two colors (RCOLOR2) and therefore not a model of RWKL. The proof combines bushy tree forcing and a technique introduced by Lerman, Solomon and Towsner to transform a computable non-reducibility into a separation over omega-models.Comment: 18 page

Current practice in project appraisal in Europe.

The work reported in this paper presents the results from the compilation of the national assessment practices in EU25 Member States and Switzerland. The work was completed as part of the current European Union 6th Framework project HEATCO (Developing Harmonised European Approaches for Transport Costing and Project Assessment), which has the objective of developing a set of harmonised guidelines for project assessment and transport costing at an EU level. This paper presents the starting point to this project. Based on the work described in this paper the HEATCO consortium will be developing common definitions and consistent valuation methods for the evaluation of TEN projects. Previous projects such as EUNET had conducted a similar review to the research presented in this paper. The key reason for repeating the research was the expansion of the EU to 25 countries in May 2004 and the fact that appraisal practices in many countries has evolved since the last survey. A proforma was designed and sent to country representatives to complete. This paper is based predominantly on the results that this data provided. The proforma focused specifically on the use of Cost Benefit Analysis in appraisal with the aim of identifying similarities and differences in country practice. Aside from the national appraisal framework the proforma also considered the individual impacts included in appraisal. The paper describes some of the similarities and differences in how construction costs, time savings, safety and environmental impacts are used across Europe. The paper then concludes with the key differences and similarities as identified by the analysis. This paper aims at providing an overview of the current appraisal practice and more country specific details are given in Odgaard et al (2005)