We prove that all valid Herbrand equalities can be interprocedurally inferred for programs where all assignments are taken into account whose right-hand sides depend on at most one variable. The analysis is based on procedure summaries representing the weakest preconditions for finitely many generic post-conditions with template variables. In order to arrive at effective representations for all...

Numerous variable selection methods rely on a two-stage procedure, where a sparsity-inducing penalty is used in the first stage to predict the support, which is then conveyed to the second stage for estimation or inference purposes. In this framework, the first stage screens variables to find a set of possibly relevant variables and the second stage operates on this set of candidate variables, ...

This paper continues the study of the two-variable fragment of first-order logic (FO2) over twodimensional structures, more precisely structures with two orders, their induced successor relations and arbitrarily many unary relations. Our main focus is on ordered data words which are finite sequences from the set Σ×D where Σ is a finite alphabet and D is an ordered domain. These are naturally re...

This paper present two variable ordering methods for minimizing Reduced Ordered Binary Decision Diagrams (ROBDDs). The broad formal techniques, based on graph topology, and the details of the algorithms are suitable for further work on other algorithms of the same family. Experiments have shown that the algorithms improve on common algorithms for the majority of benchmark circuits.

We give sign-reversing involution proofs of a pair of two variable Pfaffian identities. Applications to symmetric function theory are given, including identities relating Pfaffians and Schur functions. As a corollary we are able to compute the plethysm p2 ° skn •

We study Minkowski’s inequality Da b(x1 + x2, y1 + y2) ≤ Da b(x1, y1) +Da b(x2, y2) (x1, x2, y1, y2 ∈ R+) and its reverse where Da b is the difference mean introduced by Stolarsky. We give necessary and sufficient conditions (concerning the parameters a, b) for the inequality above (and for its reverse) to hold.

Macdonald defined in [M1] a remarkable class of symmetric polynomials Pλ(x; q, t) which depend on two parameters and interpolate between many families of classical symmetric polynomials. For example Pλ(x; t) = Pλ(x; 0, t) are the Hall-Littlewood polynomials which themselves specialize for t = 0 to Schur functions sλ. Also Jack polynomials arise by taking q = t and letting t tend to 1. The Hall-...

We study an extension of FO2[<], first-order logic interpreted in finite words, in which formulas are restricted to use only two variables. We adjoin to this language two-variable atomic formulas that say, ‘the letter a appears between positions x and y’. This is, in a sense, the simplest property that is not expressible using only two variables. We present several logics, both first-order and ...