The partially disjoint paths problem is: given: a directed graph, vertices r1, s1, . . . , rk, sk, and a set F of pairs {i, j} from {1, . . . , k}, find: for each i = 1, . . . , k a directed ri − si path Pi such that if {i, j} ∈ F then Pi and Pj are disjoint. We show that for fixed k, this problem is solvable in polynomial time if the directed graph is planar. More generally, the problem is sol...

Recently, Milner and Moller have presented several decomposition results for processes. Inspired by these, we investigate decomposition techniques for the verification of parallel systems. In particular, we consider those of the form ‖n i=1 pi = ‖mj=1 qj (I) where pi and qj are (finite) state systems. We provide a decomposition procedure for all pi and qj and give criteria that must be checked ...

in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.

We study the expressive power and complexity of second-order revised Krom logic (SO-KROM$^{r}$). On ordered finite structures, we show that its existential fragment $\Sigma^1_1$-KROM$^r$ equals $\Sigma^1_1$-KROM, captures NL. all for $k\geq 1$, $\Sigma^1_{k}$ $\Sigma^1_{k+1}$-KROM$^r$ if $k$ is even, $\Pi^1_{k}$ $\Pi^1_{k+1}$-KROM$^r$ odd. The result gives an alternative to capture polynomial h...

In the present work, we investigate several theoretical models of pion vector form factor and aim at getting best fit for two-pion cross sections to reduce uncertainties calculation contribution muon anomalous magnetic moment. Combined with a polynomial description factor, obtain from Gounaris-Sakurai (or K\"uhn-Santamaria) model experimental data up 1 GeV. By product, branching ratio $\omega \...

Definition 8.1.1 Let P = ∑ i∈J Pi. Clearly 1 ≤ OPT ≤ P . Since 1 ≤ OPT ≤ P , if we have access to a (1 + )-relaxed decision procedure we can use it O(logP ) times to do a binary search on different values of T (between 1 and P ) to find a (1 + )approximation. Since logP is polynomial in the input size, if the relaxed decision procedure runs in polynomial time then we have a (1 + )-approximation...

We study a class of two-variable polynomials called exact which contains $A$ -polynomials knot complements. The Mahler measure these can be computed in terms volume function defined on the vanishing set polynomial. prove that local extrema are two-dimensional torus and give closed formula for extremal values. This shows an irreducible polynomial divided by $\pi$ is greater than amplitude functi...

A large number of medical experiments have confirmed that the features drugs a close correlation with their molecular structure. Drug properties can be obtained by studying structure corresponding drugs. The calculation topological index chemical graph enables scientists to better understanding physical chemistry and biological characteristics In this paper, we focus on Hyaluronic Acid-Curcumin...

The question of knowing whether the policy Iteration algorithm (PI) for solving Markov Decision Processes (MDPs) has exponential or (strongly) polynomial complexity has attracted much attention in the last 50 years. Recently, Fearnley proposed an example on which PI needs an exponential number of iterations to converge. Though, it has been observed that Fearnley’s example leaves open the possib...

Suppose that $\chi_\lambda$ and $\chi_\mu$ are distinct irreducible characters of the symmetric group $S_n$. We give an algorithm that, in time polynomial $n$, constructs $\pi\in S_n$ such $\chi_\lambda(\pi)$ is provably different from $\chi_\mu(\pi)$. In fact, we show a little more. $f = \chi_\lambda$ for some character $S_n$, but do not know $\lambda$, given only oracle access to $f$. determi...