Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting.

The Third International Workshop on Parameterized and Exact Computation washeldinVictoria, B. C. duringMay14-16,2008. Theworkshopwasco-located with the 40th ACM Symposium on Theory of Computing, which took place in Victoria during May 17-20. Previousmeetings of the IWPECseries wereheld in Bergen, Norway 2004 and Zu ]rich, Switzerland 2006, both as part of the ALGO joint conference. TheInternationalWorkshoponParameterizedandExactComputationcovers research in all aspects of parameterized and exact computation and complexity, including but not limited to: new techniques for the design and analysis of - rameterizedandexactalgorithms, parameterizedcomplexitytheory, relationship betweenparameterizedcomplexityandtraditionalcomplexityclassi?cations, - plicationsofparameterizedcomputation, implementationandexperiments, hi- performancecomputing and ?xed-parametertractability. We received32 submissions. Eachsubmission wasreviewed by at least 3, and on the average 3. 9, Program Committee (PC) members. We held an electronic PC meeting using the EasyChair system. The committee decided to accept 17 papers. We would thoroughly like to thank the members of the PC: Yijia Chen, Shanghai, China Benny Chor, Tel Aviv, Israel FedorV. Fomin, Bergen, Norway Jiong Guo, Jena, Germany Gregory Gutin, London, UK MohammadTaghi Hajiaghayi, AT&T, USA Peter Jonsson, Link] oping, Sweden Iyad Kanj, Chicago, USA Dieter Kratsch, Metz, France D aniel Marx, Budapest, Hungary Prabhakar Ragde, Waterloo, Canada Kenneth W. Regan, Bu?alo, USA Ulrike Stege, Victoria, Canada Stephan Szeider, Durham, UK Todd Wareham, Newfoundland, Canada Osamu Watanabe, Tokyo, Japan and all external referees for the valuable work they put in the reviewing process. We would like to thank the three invited speakers Jianer Chen (Texas A&M University), Erik Demaine (MIT), and Stephan Kreutzer (Oxford University) for their contribution to the program of the workshop and their contributions for this proceedings volume."