We develop a polynomial translation from finite control processes (an important fragment of pi-calculus) to safe low-level Petri nets. To our knowledge, this is the first such translation. It is natural (there is a close correspondence between the control flow of the original specification and the resulting Petri net), enjoys a bisimulation result, and is suitable for practical model checking. ...

Recently, a number of interesting algorithmic problems have arisen from the emergence, in a number of countries, of kidney exchange schemes, whereby live donors are matched with recipients according to compatibility and other considerations. One such problem can be modeled by a variant of the well-known stable roommates problem in which blocking cycles, as well as the normal blocking pairs, are...

We study a special case of a structured mixed integer programming model that arises in production planning. For the most general case of the model, called PI, we have earlier identified three families of facet–defining valid inequalities: (l, S) inequalities (introduced for the uncapacitated lot–sizing problem by Barany, Van Roy, and Wolsey), cover inequalities, and reverse cover inequalities. ...

No matter how a positive semidefinite polynomial f ∈ R[X1, . . . , Xn] is represented (according to E. Artin’s 1926 solution to Hilbert’s 17th problem) in the form f = ∑ pir 2 i (with 0 ≤ pi ∈ R and ri ∈ R(X1, . . . , Xn)), the pi and the coefficients of the ri cannot be chosen to depend in a C ∞ (i.e., infinitely differentiable) manner upon the coefficients of f (unless deg f ≤ 2); formal powe...

We study polynomial identities of algebras with involution nonassociative over a field characteristic zero. prove that the growth sequence ⁎-codimensions finite-dimensional algebra is exponentially bounded. construct series fractional ⁎-PI-exponent. also family infinite-dimensional Cα such exp⁎(Cα) does not exist.

in this paper, at first we mention to some results related to pi and vertex co-pi indices and then we introduce the edge versions of co-pi indices. then, we obtain some properties about these new indices.

Given convex polytopes P1, . . . , Pr ⊂ R n and finite subsets WI of the Minkowsky sums PI = � i∈I Pi, we consider the quantityN(W) = � I⊂[r] (−1) r−|I|� WI � �. If WI = Z n ∩ PI and P1, . . . , Pn are lattice polytopes in R , then N(W) is the classical mixed volume of P1, . . . , Pn giving the number of complex solutions of a general complex polynomial system with Newton polytopes P1, . . . , ...

We consider the non-crossing connectors problem, which is stated as follows: Given n simply connected regions R1, . . . , Rn in the plane and finite point sets Pi ⊂ Ri for i = 1, . . . , n, are there non-crossing connectors γi for (Ri, Pi), i.e., arc-connected sets γi with Pi ⊂ γi ⊂ Ri for every i = 1, . . . , n, such that γi ∩ γj = ∅ for all i 6= j? We prove that non-crossing connectors do alw...