Bernd Borchert

On the acceptance power of regular languages

In [BCS92] it was shown that several well-known complexity classes which have a complete set for every relativization can be characterized by an acceptance language for the words of ouputs produced by a nondeterministic polynomial time computation. In [HL*93] some results were shown for classes for which this acceptance language is regular. Here a partial order on relativizable classes is presented which reflects the idea of oracle independent inclusion. The main result will be that this partial order on the classes characterized by regular languages is atomic and therefore not dense. The atoms correspond to the classes NP, co-NP and MODpP for p prime.

On the Computational Complexity of Some Classical Equivalence Relations on Boolean Functions

Abstract. The paper analyzes in terms of polynomial time many-one reductions the computational complexity of several natural equivalence relations on Boolean functions which derive from replacing variables by expressions, one of them is the Boolean isomorphism relation. Most of these computational problems turn out to be between co-NP and

Succinct circuit representations and leaf language classes are basically the same concept

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Looking for an Analogue of Rice's Theorem in Circuit Complexity Theory

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A characterization of the leaf language classes

This note connects two topics of complexity theory: The topic of succinct circuit representations initiated by Galperin and Wigderson (1983), and the topic of leaf language classes initiated by Bovet et al. (1992). It will be shown for any language that its succinct version is polynomial-time many-one complete for the leaf language class determined by it.

Predicate classes and promise classes

Rices Theorem says that every nontrivia semantic property of programs is undecidable. In this spirit we show the following: Every nontrivia absolute (gap, relative) counting property of circuits is UP-hard with respect to polynomial-time Turing reductions. For generators [31] we show a perfect analogue of Rices Theorem.

THE DOT-DEPTH AND THE POLYNOMIAL HIERARCHIES CORRESPOND ON THE DELTA LEVELS

Abstract Bovet, Crescenzi, and Silvestri (1992, 1995), and independently Vereshchagin (1994), showed that many complexity classes in the polynomial time setting are leaf language classes, i.e. classes which are determined by two disjoint languages. They gave many examples but they did not characterize the set of leaf language classes. This will be done in this paper. It will be shown that the set of leaf language classes equals the set of countable complexity classes that are closed downward with respect to polynomial-time many-one reducibility ⩽mp and closed under join. Moreover, the set of classes characterizable by two complementary leaf languages will be shown to be equal to the set of complexity classes which, with respect to ⩽mp, have a complete set and are closed downward.

Online Banking with NFC-Enabled Bank Card and NFC-Enabled Smartphone

Considering computation trees produced by polynomial time nondeterministic computations one can define a complexity class by any predicate on computation trees, such classes will be called predicate classes. It will be shown that these classes are exactly the principal ideals of the polynomial time many-one reducibility. Additionally, the set of classes-which are called promise classes-definable by promise functions instead of predicates are shown to be equal to the set of countable ideals.<<ETX>>

Few Product Gates But Many Zeros

It is well-known that the Σk- and Πk-levels of the dot-depth hierarchy and the polynomial hierarchy correspond via leaf languages. We extend this correspondence to the Δk-levels of these hierarchies: . The same methods are used to give evidence against an earlier conjecture of Straubing and Therien about a leaf-language upper bound for BPP.

Restrictive Acceptance Suffices for Equivalence Problems

Banks want to use their genuine strong credential for online banking transaction authorization - the debit card. Customers nowadays are usually equipped with a Smartphone and prefer to not carry a card reader in addition. Methods where developed that use the Smartphone to authorize online banking transactions. These methods are vulnerable to Smartphone malware. We present NFC-TAN as a Smartphone method that combines the two requirements: Strong credential debit card and no additional device. We discuss to what extend this solution decreases vulnerability. Moreover, we consider usability, cost, and integration aspects of NFC-TAN.