In this work, we study a class of randomized weak pseudorandom functions, which we call weak PRFs with hidden auxiliary input (HIwPRF). Compared to Learning Parity with Noise (LPN) or Learning with Errors (LWE) based randomized weak PRFs, it provides less algebraic structure such that many known techniques and constructions do not translate to this class. We investigate the potential of HIwPRFs...

This paper is a survey on the algebraic approach to the theory of automata accepting infinite words. We discuss the various acceptance modes (Büchi automata, Muller automata, transition automata, weak recognition by a finite semigroup, ω-semigroups) and prove their equivalence. We also give two algebraic proofs of McNaughton’s theorem on the equivalence between Büchi and Muller automata. Finall...

The trace inverse function Tr(x−1) over the finite field F2n is a class of very important Boolean functions in stream ciphers, which possesses many good properties, including high algebraic degree, high nonlinearity, ideal autocorrelation, etc. In this work we discuss properties of Tr(x−1) in resistance to (fast) algebraic attacks. As a result, we prove that the algebraic immunity of Tr(x−1) ar...

For a computable field F , the splitting set SF of F is the set of polynomials with coefficients in F which factor over F , and the root set RF of F is the set of polynomials with coefficients in F which have a root in F . Results of Frohlich and Shepherdson in [3] imply that for a computable field F , the splitting set SF and the root set RF are Turing-equivalent. Much more recently, in [6], M...

This paper is a study of similarities and di erences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic. In the papers concerning quant...

A method for H∞ observer design for linear time-delay systems based on the algebraic Riccati equation is proposed. A ”weak” sufficient condition for the existence of such an observer is given.

We deene weak inclusion systems as a natural extension of inclusion systems. We prove that several properties of factorisation systems and inclusion systems remain valid under this extension and we obtain new properties as algebraic tools in abstract model theory.

Weak equivalences are important behavioral equivalences in the course of specifying and analyzing reactive systems using process algebraic languages. In this paper, we propose a series of weak equivalences named weak parametric readiness equivalences, which take two previously-known behavioral equivalences, i.e., the weak readiness equivalence and the weak possible future equivalence, as their ...

A II1-factor embeds into the ultraproduct of the hyperfinite II1-factor if and only if it satisfies the von Neumann algebraic analogue of Lance’s weak expectation property (WEP). This note gives a self contained proof of this fact.

Weak direct products of arbitrary universal algebras are introduced. The usual notion for groups and rings is a special case. Some universal algebraic properties are proved and applications to cylindric and polyadic algebras are considered.