Hierarchy and Complexity

Hierarchy, Complexity, and Agent-based Models

Parameterized Circuit Complexity and the W Hierarchy

A parameterized problem 〈L, k〉 belongs to W [t] if there exists k′ computed from k such that 〈L, k〉 reduces to the weight-k′ satisfiability problem for weft-t circuits. We relate the fundamental question of whether the W [t] hierarchy is proper to parameterized problems for constant-depth circuits. We define classes G[t] as the analogues of AC depth-t for parameterized problems, and N [t] by we...

hh and a Hierarchy of Complexity Classes

One can view NP as the complexity class that captures the notion of efficient provability by classical (formal) proofs. We consider broader complexity classes (still “just above NP”), in the hope to formalize the notion of efficient provability by overwhelming statistical evidence. Such a concept should combine the nondeterministic nature of (classical) proofs and the statistical nature of conc...

Hierarchy and Complexity in Physical Systems

The discussion in this paper has to do with the uncertainty of knowledge, in particular regarding that paradigm of scientific certainty, physics. We argue that starting with the Greeks it has not been possible to predict events with absolute certainty, and even the contemporary laws of physics are in fact statistical and result in predictions that are probabilistic in character. We begin with t...

Complexity and Hierarchy in Truth Predicates∗

Since seminal work of Tarski (e.g. Tarski, 1935), hierarchies have been much discussed in the literature on truth and paradox. Especially in recent years, this discussion has been decidedly negative. Tarski’s hierarchy of languages is sometimes described as the “orthodox” response to the Liar paradox (e.g. Kripke, 1975), but it is an orthodoxy many authors have gone to great lengths to avoid. F...