In order to properly teach any subject, it is important to understand the underlying cognitive models of the learning process. Unfortunately, sometimes basic concepts are not adequately taught during primary school because primary school teachers lack the knowledge and/or the basic tools about these concepts. For instance, children have to learn to handle our standard base-10 positional numeral system. Unfortunately, teachers are not usually aware of the intrinsic difficulties of this learning process, the reason being that adults have internalized this knowledge so deep in their mental process that they usually think that it is an obvious and very natural representation. Thus, teachers have problems to understand the actual difficulties that children must confront. In this paper we present an experience we have conducted in the Education Faculty of our university to help future teachers to understand such difficulties. By using our tool, future teachers are forced to face all the steps children have to follow in their learning process. Thus, they learn the problems their future students will have, and they will be better prepared to improve the Mathematics skills of their students.

We study the problems of picking the media where a good or service is advertised in such a way the cost of placing these advertisements is minimized but, simultaneously, the individuals of some given population segments reach some minimum average advertisement impressions (views); or they reach some minimum probabilities of watching the advertisement at least once; or they reach both. The proposed model lets the publicist explicitly define the dependencies between media audience (i.e., whether viewers of some medium typically watch some other medium; or typically do not watch it; or typically watch it as the rest of the audience). We prove the Log-APX-hardness of these three problems. We present two heuristics to suboptimally solve each of these problems (one greedy and the other one based on genetic algorithms) and compare their performance for several problem instances.

In this paper we develop a general framework to reason about testing. The difficulty of testing is assessed in terms of the amount of tests that must be applied to determine whether the system is correct or not. Based on this criterion, five testability classes are presented and related. We also explore conditions that enable and disable finite testability, and their relation to testing hypotheses is studied. We measure how far incomplete test suites are from being complete, which allows us to compare and select better incomplete test suites. The complexity of finding that measure, as well as the complexity of finding minimum complete test suites, is identified. Furthermore, we address the reduction of testing problems to each other, that is, we study how the problem of finding test suites to test systems of some kind can be reduced to the problem of finding test suites for another kind of systems. This enables to export testing methods. In order to illustrate how general notions are applied to specific cases, many typical examples from the formal testing techniques domain are presented.

Abstract Given a finite state machine denoting the specification of a system, finding some short interaction sequences capable of reaching some/all states or transitions of this machine is a typical goal in testing methods. If these sequences are applied to an implementation under test , then equivalent states or transitions would be reached and observed in the implementation—provided that the implementation were actually defined as the specification. We study the problem of finding such sequences in the case where configurations previously traversed can be saved and restored (at some cost). In general, this feature enables sequences to reach the required parts of the machine in less time, because some repetitions can be avoided. However, we show that finding optimal sequences in this case is an NP-hard problem. We propose an heuristic method to approximately solve this problem based on an evolutionary computation approach, in particular river formation dynamics (RFD). Given finite state machine specifications and sets of states/transitions to be reached, we apply RFD to construct testing plans reaching these configurations. Experimental results show that being able to load previously traversed states generally reduces the time needed to cover the target configurations.

NP-complete problems are particularly hard to solve. Unless P=NP, any algorithm solving an NP-complete problem takes exponential time in the worst case. The intrinsic difficulty of NP-complete problems when we try to optimally solve them with compute

We present a tool to automatically derive choreography-conforming web services systems. The user provides a specification that describes peer-to-peer collaborations of the observable behavior of parties from a global viewpoint, in our case WS-CDL documents, and the tool automatically extracts the particular behavior of each participant, more concretely, WS-BPEL documents defining the behavior from a local viewpoint. We implement two automatic methods(centralized and decentralized) that derive conforming systems even in cases where projecting the choreography into each service would lead to a non-conforming system. This issue is addressed by adding some control messages that make services interact as required by the choreography. Experiments where the number of exchanged messages is measured are presented, and strategies to reduce the number of these messages are discussed.