The word problem for inverse monoids generated by a set Γ subject to relations of the form e = f , where e and f are both idempotents in the free inverse monoid generated by Γ , is investigated. It is shown that for every fixed monoid of this form the word problem can be solved in polynomial time which solves an open problem of Margolis and Meakin. For the uniform word problem, where the presen...

We study the following “inverse first passage time” problem. Given a diffusion process Xt and a probability distribution q on [0,∞), does there exist a boundary b(t) such that q(t) = P[τ ≤ t], where τ is the first hitting time of Xt to the time dependent level b(t). A free boundary problem for a parabolic partial differential operator is associated with the inverse first passage time problem. W...

We present a linear time algorithm for computing a cycle separator in a planar graph that is (arguably) simpler than previously known algorithms. Our algorithm builds on, and is somewhat similar to, previous algorithms for computing separators. In particular, the algorithm described by Klein and Mozes [KM17] is quite similar to ours. The main new ingredient is a specific layered decomposition o...

Every economic model should include an estimate of its stability and predictability. A new measure, the first passage time (FPT) which is defined as the time period when the model error first exceeds a pre-determined criterion (i.e., the tolerance level), is proposed here to estimate the model predictability. A theoretical framework is developed to determine the mean and variance of FPT. The cl...

In this paper, we are concerned with Reflected Geometric Brownian Motion (RGBM) with two barriers. And the stationary distribution of RGBM is derived by Markovian infinitesimal Generator method. Consequently the first passage time of RGBM is also discussed.

We determine the distributions of occupation times of a Markov-modulated Brownian motion (MMBM) in separate intervals before a first passage time or an exit from an interval. They will be derived in terms of their Laplace transforms, distinguishing occupation times in different phases too. For MMBMs with strictly positive variation parameters we further propose scale functions.

We consider equivalence relations and preorders complete for various levels of the arithmetical hierarchy under computable, component-wise reducibility. We show that implication in first order logic is a complete preorder for Σ1, the ≤m relation on EXPTIME sets for Σ2 and the embeddability of computable subgroups of (Q,+) for Σ3. In all cases, the symmetric fragment of the preorder is complete ...

Durbin (1992) derived a convergent series for the density of the first passage time of a Weiner process to a curved boundary. We show that the successive partial sums of this series can be expressed as the iterates of the standard substitution method for solving an integral equation. The calculation is thus simpler than it first appears. We also show that, under a certain condition, the series ...

We introduce the Excesses Incremental Breadth-First Search (Excesses IBFS) algorithm for maximum flow problems. We show that Excesses IBFS has the best overall practical performance on real-world instances, while maintaining the same polynomial running time guarantee of O(mn) as IBFS, which it generalizes. Some applications, such as video object segmentation, require solving a series of maximum...

In many types of planning algorithms distance heuristics play an important role. Most of the earlier works restrict to STRIPS operators, and their application to a more general language with disjunctivity and conditional effects first requires an exponential size reduction to STRIPS operators. I present direct formalizations of a number of distance heuristics for a general operator description ...