Decision Making in the Medical Domain: Comparing the Effectiveness of GP-Generated Fuzzy Intelligent Structures

ABSTRACT: In this work, we examine the effectiveness of two intelligent models in medical domains. Namely, we apply grammar-guided genetic programming to produce fuzzy intelligent structures, such as fuzzy rule-based systems and fuzzy Petri nets, in medical data mining tasks. First, we use two context-free grammars to describe fuzzy rule-based systems and fuzzy Petri nets with genetic programming. Then, we apply cellular encoding in order to express the fuzzy Petri nets with arbitrary size and topology. The models are examined thoroughly in four real-world medical data sets. Results are presented in detail and the competitive advantages and drawbacks of the selected methodologies are discussed, in respect to the nature of each application domain. Conclusions are drawn on the effectiveness and efficiency of the presented approach

Small Vertex Cover makes Petri Net Coverability and Boundedness Easier

The coverability and boundedness problems for Petri nets are known to be Expspace-complete. Given a Petri net, we associate a graph with it. With the vertex cover number k of this graph and the maximum arc weight W as parameters, we show that coverability and boundedness are in ParaPspace. This means that these problems can be solved in space O(ef(k,W)poly(n)), where ef(k,W) is some exponential function and poly(n) is some polynomial in the size of the input. We then extend the ParaPspace result to model checking a logic that can express some generalizations of coverability and boundedness.Comment: Full version of the paper appearing in IPEC 201

On the Upward/Downward Closures of Petri Nets

We study the size and the complexity of computing finite state automata (FSA) representing and approximating the downward and the upward closure of Petri net languages with coverability as the acceptance condition. We show how to construct an FSA recognizing the upward closure of a Petri net language in doubly-exponential time, and therefore the size is at most doubly exponential. For downward closures, we prove that the size of the minimal automata can be non-primitive recursive. In the case of BPP nets, a well-known subclass of Petri nets, we show that an FSA accepting the downward/upward closure can be constructed in exponential time. Furthermore, we consider the problem of checking whether a simple regular language is included in the downward/upward closure of a Petri net/BPP net language. We show that this problem is EXPSPACE-complete (resp. NP-complete) in the case of Petri nets (resp. BPP nets). Finally, we show that it is decidable whether a Petri net language is upward/downward closed

RGA users manual : version 2.3

RGA is an interpreter for a special language designed for the analysis of reachability graphs, or control flow graphs, generated from Petri nets. Although in some cases the reachability graph can become too large to be tractable, or can even be infinite, many interesting problems exist whose reachability graphs are of reasonable size. In RGA, the user has access to the names of the places in the net, and to the states of the reachability graph. The structure of the graph is also available through functions which return the sets of successor or predecessor states of a state and the transition-firings connecting the states. The RGA language allows dynamic typing of identifiers, recursion, and function and operator overloading. Rather than providing a number of predefined analysis functions, RGA provides primitive functions which allow the user to conduct complex analyses with little programming effort. RGA is part of a suite of tools, called P-NUT, intended to facilitate the analysis of concurrent systems described by Petri nets

Phase ordering and symmetries of the Potts model

We have studied the ordering of the q-colours Potts model in two dimensions on a square lattice. On the basis of our observations we propose that if q is large enough the system is not able to break global and local null magnetisation symmetries at zero temperature: when q<4 the system forms domains with a size proportional to the system size while for q>4 it relaxes towards a non-equilibrium phase with energy larger than the ground state energy, in agreement with the previous findings of De Oliveira et al. (M. J. de Oliveira, A. Petri, T. Tome, Europhys. Lett., 65, 20 (2004)).Comment: 6 pages, 3 figures; minor text rewordings and changes in figures styl