Machine Models and Simulation.

TL;DR: This chapter discusses the concepts needed for defining the complexity classes, a set of problems of related resource-based complexity that can be solved by an abstract machine M using O(f(n) of resource R, where n is the size of the input.

TL;DR: It is shown that unless PTIME=NP, the model-checking problem for monadic second-order logic on finite words is not solvable in time f(k)/spl middot/p(n), for any elementary function f and any polynomial p, and under an assumption from parameterized complexity theory.

TL;DR: A taxonomy that classifies multi-agent systems according to communication, computational and other capabilities is presented, and it is demonstrated that a collective can be demonstrably more powerful than a single unit of the collective.

TL;DR: It is shown that for each property φ of structures that is definable in first-order logic and for each locally tree-decomposable class C of structures, there is a linear time algorithm deciding whether a given structure A ∈ C hasproperty φ.