Boolean function

Abstract: A description is given of linear and disjoint decompositions of completely specified Boolean functions using transform methods. Since previously known transform methods are impractical for automation due to their enormous computational complexity, polynomial approximations to the linear decomposition procedure that use reduced representations of functions are used. Experimental results are reported which establish that such decompositions can often result in improved implementations of logic functions. The disjoint decomposition problem is in the spectral domain, allowing the development of an algorithm that can simultaneously detect multiple decompositions of a given function. This algorithm has low average complexity and has the ability to detect the nonexistence of decompositions quickly. >

Abstract: Minimal pairs for polynomial time reducibilities.- Primitive recursive word-functions of one variable.- Existential fixed-point logic.- Unsolvable decision problems for PROLOG programs.- You have not understood a sentence, unless you can prove it.- On the minimality of K, F, and D or: Why loten is non-trivial.- A 5-color-extension-theorem.- Closure relations, Buchberger's algorithm, and polynomials in infinitely many variables.- The benefit of microworlds in learning computer programming.- Skolem normal forms concerning the least fixpoint.- Spectral representation of recursively enumerable and coenumerable predicates.- Aggregating inductive expertise on partial recursive functions.- Domino threads and complexity.- Modelling of cooperative processes.- A setting for generalized computability.- First-order spectra with one variable.- On the early history of register machines.- Randomness, provability, and the separation of Monte Carlo Time and space.- Representation independent query and update operations on propositional definite Horn formulas.- Direct construction of mutually orthogonal latin squares.- Negative results about the length problem.- Some results on the complexity of powers.- The Turing complexity of AF C*-algebras with lattice-ordered KO.- Remarks on SASL and the verification of functional programming languages.- Numerical stability of simple geometric algorithms in the plane.- Communication with concurrent systems via I/0-procedures.- A class of exp-time machines which can be simulated by polytape machines.- ???-Automata realizing preferences.- Ein einfaches Verfahren zur Normalisierung unendlicher Herleitungen.- Grammars for terms and automata.- Relative konsistenz.- Segment translation systems.- First steps towards a theory of complexity over more general data structures.- On the power of single-valued nondeterministic polynomial time computations.- A concatenation game and the dot-depth hierarchy.- Do there exist languages with an arbitrarily small amount of context-sensitivity?.- The complexity of symmetric boolean functions.

Abstract: Secure multi-party computation (MPC) is an active research area, and a wide range of literature can be found nowadays suggesting improvements and generalizations of existing protocols in various directions. However, all current techniques for secure MPC apply to functions that are represented by (boolean or arithmetic) circuits over finite fields. We are motivated by two limitations of these techniques: - GENERALITY. Existing protocols do not apply to computation over more general algebraic structures (except via a brute-force simulation of computation in these structures). - EFFICIENCY. The best known constant-round protocols do not efficiently scale even to the case of large finite fields. Our contribution goes in these two directions. First, we propose a basis for unconditionally secure MPC over an arbitrary finite ring, an algebraic object with a much less nice structure than a field, and obtain efficient MPC protocols requiring only a black-box access to the ring operations and to random ring elements. Second, we extend these results to the constant-round setting, and suggest efficiency improvements that are relevant also for the important special case of fields. We demonstrate the usefulness of the above results by presenting a novel application of MPC over (non-field) rings to the round-efficient secure computation of the maximum function.

Abstract: Determining the equivalence of reversible circuits designed to meet a common specification is considered. The circuits' primary inputs and outputs must be in pure logic states but the circuits may include elementary quantum gates in addition to reversible logic gates. The specification can include don't-cares arising from constant inputs, garbage outputs, and total or partial don't-cares in the underlying target function. The paper explores well-known techniques from irreversible equivalence checking and how they can be applied in the domain of reversible circuits. Two approaches are considered. The first employs decision diagram techniques and the second uses Boolean satisfiability. Experimental results show that for both methods, circuits with up to 27,000 gates, as well as adders with more than 100 inputs and outputs, are handled in under three minutes with reasonable memory requirements.