Faculty Scholarship

Two algorithms in search of a type system

Norman Danner et al. — Wed, 29 May 2013 13:03:48 PDT

The authors’ ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR -definable ( ATR types are confined to levels 0, 1, and 2). A limitation of the original version of ATR is that the only directly expressible recursions are tail-recursions. Here we extend ATR so that a broad range of affine recursions are directly expressible. In particular, the revised ATR can fairly naturally express the classic insertion- and selection-sort algorithms, thus overcoming a sticking point of most prior implicit-complexity-based formalisms. The paper’s main work is in refining the original time-complexity semantics for ATR to show that these new recursion schemes do not lead out of the realm of feasibility.

A static cost analysis for a higher-order language

Norman Danner et al. — Tue, 09 Oct 2012 07:30:38 PDT

We develop a static complexity analysis for a higher-order functional language with structural list recursion. The complexity of an expression is a pair consisting of a cost and a potential. The former is defined to be the size of the expression's evaluation derivation in a standard big-step operational semantics. The latter is a measure of the "future" cost of using the value of that expression. A translation function ||.|| maps target expressions to complexities. Our main result is the following Soundness Theorem: If t is a term in the target language, then the cost component of ||t|| is an upper bound on the cost of evaluating t. The proof of the Soundness Theorem is formalized in Coq, providing certified upper bounds on the cost of any expression in the target language.

Effectiveness and detection of denial of service attacks in Tor

Norman Danner et al. — Wed, 01 Aug 2012 06:38:48 PDT

Tor is one of the more popular systems for anonymizing near-real-time communications on the Internet. Borisov et al. [2007] proposed a denial-of-service-based attack on Tor (and related systems) that significantly increases the probability of compromising the anonymity provided. In this article, we analyze the effectiveness of the attack using both an analytic model and simulation. We also describe two algorithms for detecting such attacks, one deterministic and proved correct, the other probabilistic and verified in simulation.