The Complexity of Planning Revisited - A Parameterized Analysis

The early classifications of the computational complexity of planning under various restrictions in STRIPS (Bylander) and SAS+ (Baeckstroem and Nebel) have influenced following research in planning in many ways. We go back and reanalyse their subclasses, but this time using the more modern tool of parameterized complexity analysis. This provides new results that together with the old results give a more detailed picture of the complexity landscape. We demonstrate separation results not possible with standard complexity theory, which contributes to explaining why certain cases of planning have seemed simpler in practice than theory has predicted. In particular, we show that certain restrictions of practical interest are tractable in the parameterized sense of the term, and that a simple heuristic is sufficient to make a well-known partial-order planner exploit this fact.Comment: (author's self-archived copy

Automatic identification of causal knowledge and causal graphs in technical systems of process ventilators

U ovom radu je dan pristup automatskog računarskog identificiranja uzročnog znanja i uzročnih grafova putem monitoringa vibracija i temperatura postrojenja procesnih ventilatora velikih snaga i velikih brzina vrtnje. Predstavljena je metoda Granger-ove uzročne analize uzročnih veza mjernih parametara vibracija i temperature. Ova metoda poboljšava dijagnostiku procesnih ventilatora zbog identifikacije uzročnih zakonitosti parametara vibracija i temperatura u dijagramskom obliku. Nakon računanja i crtanja uzročnog grafa za vibracije i temperature, računa se uzročna gustoća, kao mjera dinamičke složenosti sustava. Numeričke vrijednosti uzročne gustoće se uzimaju kao indikatori sustavnog "zdravlja" procesnih ventilatora.This research paper presents the approach of automated computerized identification of causal knowledge and causal graphs using monitoring of vibrations and temperatures of sliding bearings of high-power and high-speed process ventilators. Method of Granger causal connectivity analysis of vibration and temperature parameters is presented. This method improves diagnostics of process ventilators because of identification of causal relations and links of vibrations and temperatures in graph form. After computing and plotting causal graphs for vibrations and temperatures, causal density is computed as a measure of dynamical complexity of system. Numerical values of causal density are taken as indicators of systems "health" of process ventilators

The Influence of k-Dependence on the Complexity of Planning

A planning problem is k-dependent if each action has at most k pre-conditions on variables unaffected by the action. This concept is well-founded since k is a constant for all but a few of the standard planning domains, and is known to have implications for tractability. In this paper, we present several new complexity results for P(k), the class of k-dependent planning problems with binary variables and polytree causal graphs. The problem of plan generation for P(k) is equivalent to determining how many times each variable can change. Using this fact, we present a polytime plan generation algorithm for P(2) and P(3). For constant k> 3, we introduce and use the notion of a cover to find conditions under which plan generation for P(k) is polynomial

Geometric auxetics

We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We demonstrate its usefulness by predicting or recognizing, without experiment, computer simulations or numerical approximations, the auxetic capabilities of several well-known structures available in the literature. We propose new principles of auxetic design and rely on the stronger notion of expansive behavior to provide an infinite supply of planar auxetic mechanisms and several new three-dimensional structures