Developments in implicit computational complexity

Quantum implicit computational complexity

We introduce a quantum lambda calculus inspired by Lafont’s Soft Linear Logic and capturing the polynomial quantum complexity classes EQP, BQP and ZQP. The calculus is based on the ‘‘classical control and quantum data’’ paradigm. This is the first example of a formal systemcapturing quantumcomplexity classes in the spirit of implicit computational complexity — it is machine-free and no explicit...

A Short Introduction to Implicit Computational Complexity

These lecture notes are meant to serve as a short introduction to implicit computational complexity for those students who have little or no knowledge of recursion theory and proof theory. They have been obtained by enriching and polishing a set of notes the author wrote for a course (on the same subject) he gave at ESSLLI 2010. These notes are definitely not meant to be comprehensive nor exhau...

Resource analysis and implicit computational complexity

Implicit computational complexity (ICC) studies machine-independent approaches to computational complexity, with emphasis on approaches based on mathematical logic. Most work consists in characterizations of complexity classes by logical systems (via the Curry-Howard correspondence). Unfortunately, all these formal systems have been studied with different, often unrelated methodologies, and few...

Probabilistic Recursion Theory and Implicit Computational Complexity

In this thesis we provide a characterization of probabilistic computation in itself, from a recursion-theoretical perspective, without reducing it to deterministic computation. More specifically, we show that probabilistic computable functions, i.e., those functions which are computed by Probabilistic Turing Machines (PTM), can be characterized by a natural generalization of Kleene’s partial re...

Implicit Computational Complexity ESSLLI 2010 CPH