For clique, typically one has a parameter k, and the problem is to check whether a clique of size k … See more

∀x X(x) ↔ ¬Y (x) ∀x ∀y (X(x) ∧ Y (y) → ∀x (X(x) → A(x) ∧ Y (x) x < y)  ∧ ∧ → B(x))   When is Ms a model of Φ? This happens iff there exists two sets of posi-tions, X an… See more

This sentence says that the universe {1, . . ., n} can be partitioned into two sets X and Y such that 1 ∈ X, n ∈ Y , and the successor of an element of X is in Y and vice versa; … See more

In Chap. 2, we review the background material from mathematical logic, com-putability theory, and complexity theory. In Chap. 3 we introduce the fundamental tool of Ehrenfeu… See more

Let L be a language accepted by a halting Turing machine M. Assume that for some function f : N → N, it is the case that the number of transitions M makes before accepting o… See more