For uniform meshes it is shown that any linear fc-step formula can be formulated so that only k values need to be saved between steps. By saving additional m values it is possible to construct local polynomial approximations of degree k + m — 1, which can be used as predictor formulas. Different polynomial bases lead to different equivalent forms of multistep formulas. In particular, local mono...

The equilibria of strategic games with many semi-anonymous players have a strong ex-post Nash property. Even with perfect hindsight about the realized types and selected actions of all his opponents, no player has an incentive to revise his own chosen action. This is illustrated for normal form and for one shot Baysian games with statistically independent types, provided that a certain continui...

With rapidly increasing community, a plethora of conferences related to Natural Language Processing and easy access to their proceedings make it essential to check the integrity and novelty of the new submissions. This study aims to investigate the trends of text reuse in the ACL submissions, if any. We carried a set of analyses on two spans of five years papers (the past and the present) of AC...

Many combinatorial optimisation problems can be modelled as integer linear programs. We consider a class of generalised integer programs where the constraints are allowed to be taken from a broader set of relations (instead of just being linear inequalities). The set of allowed relations is defined using a many-valued logic and the resulting class of relations have provably strong modelling pro...

The famous problem of determining all perfect powers in the Fibonacci sequence (Fn)n≥0 and in the Lucas sequence (Ln)n≥0 has recently been resolved [10]. The proofs of those results combine modular techniques from Wiles’ proof of Fermat’s Last Theorem with classical techniques from Baker’s theory and Diophantine approximation. In this paper, we solve the Diophantine equations Ln = qy, with a > ...

We establish a characterization of adequate knots in terms of the degree of their colored Jones polynomial. We show that, assuming the Strong Slope conjecture, our characterization can be reformulated in terms of “Jones slopes” of knots and the essential surfaces that realize the slopes. For alternating knots the reformulated characterization follows by recent work of J. Greene and J. Howie. 20...

In the paper “Relating Strong Behavioral Equivalences for Processes with Nondeterminism and Probabilities” to appear in Theoretical Computer Science, we present a comparison of behavioral equivalences for nondeterministic and probabilistic processes. In particular, we consider strong trace, failure, testing, and bisimulation equivalences. For each of these groups of equivalences, we examine the...

We introduce a first-order model of imperative sequential programs and set up formally the unification problem in this model: given a pair of programs π1 and π2 find a pair of substitutions (θ1, θ2) such that the instances π1θ1 and π2θ2 of these programs are equivalent, i.e. compute the same function. Since functional equivalence of programs is undecidable, we choose its decidable approximation...

We shall show that the consistency of CH+¬(+) and CH+(+)+there are no club guessing sequences on ω1. We shall also prove that ♢ does not imply the existence of a strong club guessing sequence on ω1. §0. Introduction. The principle (+) and its variations were first considered by the second author in [2]. They are very weak club guessing principles. The properties of the principles were largely u...

In this paper we present a new dataset and simulator e-QRAQ (explainable Query, Reason, and Answer Question) in which a User simulator provides an Agent with a short, ambiguous story and a challenge question about the story. The story is ambiguous because some of the entities have been replaced by variables. At each turn the Agent may ask for the value of a variable or try to answer the challen...