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Recent documents in Faculty Scholarshipen-usMon, 22 Jul 2013 12:44:26 PDT3600Adventures in time and space
http://wesscholar.wesleyan.edu/compfacpub/8
http://wesscholar.wesleyan.edu/compfacpub/8Tue, 09 Jul 2013 08:35:14 PDT
This paper investigates what is essentially a call-by-value version of PCF under a complexity-theoretically motivated type system. The programming formalism, ATR1, has its first-order programs characterize the poly-time computable functions, and its second-order programs characterize the type-2 basic feasible functionals of Mehlhorn and of Cook and Urquhart. (The ATR1-types are confined to levels 0, 1, and 2.) The type system comes in two parts, one that primarily restricts the sizes of values of expressions and a second that primarily restricts the time required to evaluate expressions. The size-restricted part is motivated by Bellantoni and Cook's and Leivant's implicit characterizations of poly-time. The time-restricting part is an affine version of Barber and Plotkin's DILL. Two semantics are constructed for ATR1. The first is a pruning of the naïve denotational semantics for ATR1. This pruning removes certain functions that cause otherwise feasible forms of recursion to go wrong. The second semantics is a model for ATR1's time complexity relative to a certain abstract machine. This model provides a setting for complexity recurrences arising from ATR1 recursions, the solutions of which yield second-order polynomial time bounds. The time-complexity semantics is also shown to be sound relative to the costs of interpretation on the abstract machine.
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Norman Danner et al.Stratified polymorphism and primitive recursion
http://wesscholar.wesleyan.edu/compfacpub/7
http://wesscholar.wesleyan.edu/compfacpub/7Tue, 09 Jul 2013 08:35:13 PDT
Natural restrictions on the syntax of the second-order (i.e., polymorphic) lambda calculus are of interest for programming language theory. One of the authors showed in Leivant (1991) that when type abstraction in that calculus is stratified into levels, the definable numeric functions are precisely the super-elementary functions (level [script E]_{4} in the Grzegorczyk Hierarchy). We define here a second-order lambda calculus in which type abstraction is stratified to levels up to ω^{ω}, an ordinal that permits highly uniform (and finite) type inference rules. Referring to this system, we show that the numeric functions definable in the calculus using ranks < ω^{[script l]} are precisely Grzegorczyk's class [script E]_{[script l]+3} ([script l] ≥ 1). This generalizes Leivant (1991), where this is proved for [script l] = 1. Thus, the numeric functions definable in our calculus are precisely the primitive recursive functions.
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Norman Danner et al.Adventures in time and space
http://wesscholar.wesleyan.edu/compfacpub/6
http://wesscholar.wesleyan.edu/compfacpub/6Mon, 08 Jul 2013 10:40:15 PDT
This paper investigates what is essentially a call-by-value version of PCF under a complexity-theoretically motivated type system. The programming formalism, ATR, has its first-order programs characterize the polynomial-time computable functions, and its second-order programs characterize the type-2 basic feasible functionals of Mehlhorn and of Cook and Urquhart. (The ATR-types are confined to levels 0, 1, and 2.) The type system comes in two parts, one that primarily restricts the sizes of values of expressions and a second that primarily restricts the time required to evaluate expressions. The size-restricted part is motivated by Bellantoni and Cook's and Leivant's implicit characterizations of polynomial-time. The time-restricting part is an affine version of Barber and Plotkin's DILL. Two semantics are constructed for ATR. The first is a pruning of the naive denotational semantics for ATR. This pruning removes certain functions that cause otherwise feasible forms of recursion to go wrong. The second semantics is a model for ATR's time complexity relative to a certain abstract machine. This model provides a setting for complexity recurrences arising from ATR recursions, the solutions of which yield second-order polynomial time bounds. The time-complexity semantics is also shown to be sound relative to the costs of interpretation on the abstract machine.
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Norman Danner et al.Circuit principles and weak pigeonhole variants
http://wesscholar.wesleyan.edu/compfacpub/5
http://wesscholar.wesleyan.edu/compfacpub/5Mon, 08 Jul 2013 10:40:14 PDT
This paper considers the relational versions of the surjective, partial surjective, and multifunction weak pigeonhole principles for PV, , , and formulas as well as relativizations of these formulas to higher levels of the bounded arithmetic hierarchy. We show that the partial surjective weak pigeonhole principle for formulas implies that for each k there is a string of length 2^{2nk} which is hard to block-recognize by circuits of size n^{k}. These principles in turn imply the partial surjective principle for formulas. We show that the surjective weak pigeonhole principle for formulas in implies our hard-string principle which in turn implies the surjective weak pigeonhole principle for formulas. We introduce a class of predicates corresponding to poly-log length iterates of polynomial time computable predicates and show that over, the multifunction weak pigeonhole principle for such predicates is equivalent to an “iterative” circuit block-recognition principle. A consequence of this is that if proves this principle then RSA is vulnerable to polynomial time attacks.
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Chris Pollett et al.Simulation of circuit creation in Tor: Preliminary results
http://wesscholar.wesleyan.edu/compfacpub/4
http://wesscholar.wesleyan.edu/compfacpub/4Wed, 03 Jul 2013 13:40:26 PDT
We describe a methodology for simulating Tor relay up/down behavior over time and give some preliminary results.
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William Higginson Branin Boyd et al.Two algorithms in search of a type system
http://wesscholar.wesleyan.edu/compfacpub/3
http://wesscholar.wesleyan.edu/compfacpub/3Wed, 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.
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Norman Danner et al.A static cost analysis for a higher-order language
http://wesscholar.wesleyan.edu/compfacpub/2
http://wesscholar.wesleyan.edu/compfacpub/2Tue, 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.
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Norman Danner et al.Effectiveness and detection of denial of service attacks in Tor
http://wesscholar.wesleyan.edu/compfacpub/1
http://wesscholar.wesleyan.edu/compfacpub/1Wed, 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.
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Norman Danner et al.