We apply to Petri net theory the technique of polynomial-time many-one reductions. We study boundedness, reachability, deadlock , liveness problems and some of their variations. We derive three main results. Firstly, we highlight the power of expression of reachability which can polynomially give evidence of unboundedness. Secondly, we prove that reachability and deadlock are polynomially-time ...

We apply to Petri net theory the technique of polynomial-time many-one reductions. We study boundedness, reachability, deadlock , liveness problems and some of their variations. We derive three main results. Firstly, we highlight the power of expression of reachability which can polynomially give evidence of unboundedness. Secondly, we prove that reachability and deadlock are polynomially-time ...

Throughout this paper P,(x) will denote a polymonial of degree n ; c, c 1 c 2 ," . will denote positive absolute constants not necessarily the same if they occur at different places . Tn other words : for no choice of the points X 1 ,"',Xn can we deduce from the boundedness of I Pn _ 1(x) I, 1 <_ 15 n the boundedness of I P,,,(x) I in the whole interval ( 1, + 1) . Bernstein [1] asked himself t...

SPACES, AND NORMS OF WEIGHTED COMPOSITION OPERATORS MICHAEL T. JURY Abstract. We prove that the norm of a weighted composition operator on the Hardy space H2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on H2, and ...

One of the remarkable things about this theorem is the way in which it suggests that geometry informs arithmetic. The geometric genus g is a manifestly geometric condition, yet it is controlling what seems to be an arithmetic property. Why should the number of integral solutions to xn + yn = zn have anything to do with the shape of the complex solutions? You might argue that that the genus is e...

In this paper, an observer based fuzzy adaptive controller (FAC) is designed fora class of large scale systems with non-canonical non-affine nonlinear subsystems. It isassumed that functions of the subsystems and the interactions among subsystems areunknown. By constructing a new class of state observer for each follower, the proposedconsensus control method solves the problem of unmeasured sta...

A positive rst-order formula is bounded if the sequence of its stages converges to the least xed point of the formula within a xed nite number of steps independent of the input structure. The boundedness problem for a fragment L of rst-order logic is the following decision problem: given a positive formula in L, is it bounded? In this paper, we investigate the boundedness problem for two-variab...

We address the strategy problem for parity games with partial information and observable colors, played on finite graphs of bounded graph complexity. We consider several measures for the complexity of graphs and analyze in which cases, bounding the measure decreases the complexity of the strategy problem on the corresponding classes of graphs. We prove or disprove that the usual powerset constr...

In this paper, we introduce the  probabilistic normed groups. Among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

The aim of this paper is to prove the Uniform Boundedness Principle and Banach-Steinhaus Theorem for anti linear operators and hence strong linear operators on Banach hypervector spaces. Also we prove the continuity of the product operation in such spaces.