On the expressive power of planar perfect matching and permanents of bounded treewidth matrices

Valiant introduced some 25 years ago an algebraic model of computation along with the complexity classes VP and VNP, which can be viewed as analogues of the classical classes P and NP. They are defined using non-uniform sequences of arithmetic circuits and provides a framework to study the complexity for sequences of polynomials. Prominent examples of difficult (that is, VNP-complete) problems in this model includes the permanent and hamiltonian polynomials. While the permanent and hamiltonian polynomials in general are difficult to evaluate, there have been research on which special cases of these polynomials admits efficient evaluation. For instance, Barvinok has shown that if the underlying matrix has bounded rank, both the permanent and the hamiltonian polynomials can be evaluated in polynomial time, and thus are in VP. Courcelle, Makowsky and Rotics have shown that for matrices of bounded treewidth several difficult problems (including evaluating the permanent and hamiltonian polynomials) can be solved efficiently. An earlier result of this flavour is Kasteleyn's theorem which states that the sum of weights of perfect matchings of a planar graph can be computed in polynomial time, and thus is in VP also. For general graphs this problem is VNP-complete. In this paper we investigate the expressive power of the above results. We show that the permanent and hamiltonian polynomials for matrices of bounded treewidth both are equivalent to arithmetic formulas. Also, arithmetic weakly skew circuits are shown to be equivalent to the sum of weights of perfect matchings of planar graphs.Comment: 14 page

Inferring a shape grammar: translating designer's knowledge

This article focuses on a shape grammar that was developed to enable the adaptation of existing houses – “rabo-de-bacalhau” housing style - to new requirements and most particular on the process of inference of the grammar. Along the article we describe the process undertaken to develop the grammar and what the achievements of the transformation grammar are regarding the possibilities of a mass customization of dwelling’s rehabilitation work. The goal of this article is to describe and discuss how the designer’s knowledge was encoded into shape rules. The process used to extract the architect’s knowledge and to incorporate it into the transformation grammar enable to abstract the designer’s actions and to define a sequence of actions that can define a possible strategy of design. The proposed design methodology generates dwelling layouts that are legal since they follow the grammar language and adequate since they meet the a priori user and design requirements.info:eu-repo/semantics/acceptedVersio

Computer-aided exploration of architectural design spaces: a digital sketchbook

Het ontwerpproces van architecten vormt vaak geen lineair pad van ontwerpopgave tot eindresultaat, maar wordt veeleer gekenmerkt door exploratie of het doorzoeken van meerdere alternatieven in een (conceptuele) ontwerpruimte. Dit proces wordt in de praktijk vaak ondersteund door manueel schetsen, waarbij de ontwerpers schetsboek kan gelezen worden als een reeks exploraties. Dit soort interactie met de ontwerpruimte wordt in veel mindere mate ondersteund door hedendaagse computerondersteunde ontwerpsystemen. De metafoor van een digitaal schetsboek, waarbij menselijke exploratie wordt versterkt door de (reken)kracht van een computer, is het centrale onderzoeksthema van dit proefschrift. Hoewel het opzet van een ontwerpruimte op het eerste gezicht schatplichtig lijkt aan het onderzoeksveld van de artificiële intelligentie (AI), wordt het ontwerpen hier ruimer geïnterpreteerd dan het oplossen van problemen. Als onderzoeksmethodologie worden vormengrammatica’s ingezet, die enerzijds nauw aanleunen bij de AI en een formeel raamwerk bieden voor de exploratie van ontwerpruimtes, maar tegelijkertijd ook weerstand bieden tegen de AI en een vorm van visueel denken en ambiguïteit toelaten. De twee bijhorende onderzoeksvragen zijn hoe deze vormengrammatica’s digitaal kunnen worden gerepresenteerd, en op welke manier de ontwerper-computer interactie kan gebeuren. De resultaten van deze twee onderzoeksvragen vormen de basis van een nieuw hulpmiddel voor architecten: het digitaal schetsboek

A transformation grammar-based methodology for housing rehabilitation: meeting contemporary functional and ICT requirements

This research starts from the premise that the future of the real estate market in Portugal will require the rehabilitation of existing residential areas in order to respond to new life-styles and dwelling requirements that have emerged in an era in which information plays a structuring role in society. The goal of this research is the definition of design guidelines and a rehabilitation methodology to support architects involved in the process of adapting existing dwellings, allowing them to balance sustainability requirements and economic feasibility with new dwelling trends such as the incorporation and updating of Information Communication and Automation Technologies and the need to solve emerging conflicts affecting the use of space prompted by the introduction of new functions associated with such technologies. In addition to defining a general methodology applicable to all the building types, the study focuses on a specific type, called “rabo-de-bacalhau” (“cod-tail”), built in Lisbon between 1945 and 1965 for which a specifc methodology has been generated. Both shape grammar and space syntax were used as part of the rehabilitation methodology as tools to identify and encode the principles and rules behind the adaptation of existing houses to new requirements.FCT PhD Gran

Separable graphs, planar graphs and web grammars

This paper is concerned with the class of “web grammars,≓ introduced by Pfaltz and Rosenfeld, whose languages are sets of labelled graphs. A slightly modified definition of web grammar is given, in which the rewriting rules can have an applicability condition, and it is proved that, in general, this extension does not increase the generative power of the grammar. This extension is useful, however, for otherwise it is not possible to incorporate negative contextual conditions into the rules, since the context of a given vertex can be unbounded. A number of web grammars are presented which define interesting classes of graphs, including unseparable graphs, unseparable planar graphs and planar graphs. All the grammars in this paper use “normal embeddings≓ in which the connections between the web that is written and the host web are conserved, so that any rewriting rule affects the web only locally