The Orbit Problem consists of determining, given a linear transformation A on Q, together with vectors x and y, whether the orbit of x under repeated applications of A can ever reach y. This problem was famously shown to be decidable by Kannan and Lipton in the 1980s. In this paper, we are concerned with the problem of synthesising suitable invariants P ⊆ R, i.e., sets that are stable under A a...

We consider polyhedral versions of Kannan and Lipton's Orbit Problem [14, 13] determining whether a target polyhedron V may be reached from a starting point x under repeated applications of a linear transformation A in an ambient vector space Q. In the context of program veri cation, very similar reachability questions were also considered and left open by Lee and Yannakakis in [15], and by Bra...

Hunain Alam ([email protected]) Amruta V Bhate ([email protected]) Prakash Gangadaran ([email protected]) Sharda S Sawant ([email protected]) Shimul Salot ([email protected]) Lalit Sehgal ([email protected]) Prerana P Dange ([email protected]) Devendra A Chaukar ([email protected]) Anil K D’cruz ([email protected]) Sadhna Kannan ([email protected]) ...

Shenyang Li, Nithya Mariappan, Judit Megyesi, Brian Shank, Krishnaswamy Kannan, Sue Theus, Peter M. Price, Jeremy S. Duffield, and Didier Portilla Division of Nephrology, University of Arkansas for Medical Sciences, Little Rock, Arkansas; Division of Rheumatology, Department of Internal Medicine, University of Arkansas for Medical Sciences, Little Rock, Arkansas; Central Arkansas Veterans Healt...

First drafts prepared by Dr Germaine Buck Louis, Bethesda, USA; Dr Terri Damstra, Research Triangle Park, USA; Dr Fernando DíazBarriga, San Luis Potosi, Mexico; Dr Elaine Faustman, Washington, USA; Dr Ulla Hass, Soborg, Denmark; Dr Robert Kavlock, Research Triangle Park, USA; Dr Carole Kimmel, Washington, USA; Dr Gary Kimmel, Silver Spring, USA; Dr Kannan Krishnan, Montreal, Canada; Dr Ulrike L...

In this paper we introduce a polynomial time algorithm that solves both the conjugacy decision and search problems in free abelian-by-infinite cyclic groups where the input is elements in normal form. We do this by adapting the work of Bogopolski, Martino, Maslakova, and Ventura in [1] and Bogopolski, Martino, and Ventura in [2], to free abelian-by-infinite cyclic groups, and in certain cases a...

We show that MAEXP, the exponential time version of the Merlin-Arthur class, does not have polynomial size circuits. This significantly improves the previous known result due to Kannan since we furthermore show that our result does not relativize. This is the first separation result in complexity theory that does not relativize. As a corollary to our separation result we also obtain that PEXP, ...

Novel cyclic contractions of the Kannan and Chatterjea type are presented in this study. With aid these brand-new contractions, new results for existence uniqueness fixed points setting complete generalized metric space have been established. Importantly, generalizations extensions point theorems by their cyclical expansions that found literature. Additionally, several existing on will be work....