We study the problem of existence of (nontrivial) perfect codes in the discrete n-simplex ∆` := {( x0, . . . , xn ) : xi ∈ Z+, ∑ i xi = ` } under `1 metric. The problem is motivated by the so-called multiset codes, which have recently been introduced by the authors as appropriate constructs for error correction in the permutation channels. It is shown that e-perfect codes in the 1-simplex ∆` ex...

We consider the problem of reconstructing a set of real numbers up to translation from the multiset of its subsets of fixed size, given up to translation. This is impossible in general: for instance almost all subsets of Z contain infinitely many translates of every finite subset of Z. We therefore restrict our attention to subsets of R which are locally finite; those which contain only finitel...

In this work we consider modeling of services with workflow modules, which are a subclass of Petri nets. The service compatibility problem is to answer the question, whether two Web services fit together, i.e. whether the composed system is sound. We study complementarity of service produced/consumed resources, that is a necessary condition for the service compatibility. Resources, which are pr...

We derive the duality relation for the Hilbert series H (d; z) of almost symmetric numerical semigroup S (d) combining it with its dual H ( d; z ) . On this basis we establish the bijection between the multiset of degrees of the syzygy terms and the multiset of the gaps Fj , generators di and their linear combinations. We present the relations for the sums of the Betti numbers of even and odd i...

The stream cipher SNOW 3G designed in 2006 by ETSI/SAGE is a base algorithm for the second set of 3GPP confidentiality and integrity algorithms. In this paper we study the resynchronization mechanism of SNOW 3G and of a similar cipher SNOW 3G⊕ using multiset collision attacks. For SNOW 3G we show a simple 13-round multiset distinguisher with complexity of 2 steps. We show full key recovery chos...

Sign patterns consisting of some positive and some negative columns, with at least one of each kind, are shown to allow any self-conjugate spectrum, and thus to allow any inertia. In the case of the n× n sign pattern with all columns positive, given any self-conjugate multiset consisting of n−1 complex numbers supplemented by a sufficiently large positive number, it is shown how to construct a ...

This paper proposes grammars for visual languages. The proposed grammars introduce relations into the constraint multiset grammars[4J. Relations are the constraints on the relationships among symbols in visual languages. The proposed grammars. which are called constraint relation multiset grammars. have the relations as the first class citizens of the grammars because the relationships among sy...