Many popular algorithms that work with Boolean functions are dramatically dependent on the order of variables in input representations of Boolean functions. Such algorithms include satisfiability (SAT) solvers that are critical in formal verification and Binary Decision Diagrams (BDDs) manipulation algorithms that are increasingly popular in synthesis and verification. Finding better variable-o...

The problem of finding an optimal variable ordering for Binary Decision Diagrams (BDD) or Multi-Valued Decision Diagrams (MDD) is widely known to be NP-Complete. This paper presents a survey of static heuristic techniques applied to ordering the variables of the BDD/MDD under construction in order to minimize the overall size of the resulting decision diagram.

Recent years have witnessed a renewal of interest in variable morph ordering, the situation where the position of a morph in the word is not constant. These situations present a challenge to extant inferential-realisational approaches to morphology (Stump, 2001), insofar as these adopt implicitly or explicitly an a-morphous approach to morphological composition (Anderson, 1992). In this paper w...

The paper evaluates the e ectiveness of learning for speeding up the solution of constraint satisfaction problems. It extends previous work (Dechter 1990) by introducing a new and powerful variant of learning and by presenting an extensive empirical study on much larger and more di cult problem instances. Our results show that learning can speed up backjumping when using either a xed or dynamic...

We study a single-period inventory control problem with two independent suppliers. With the first supplier, the buyer incurs a high variable cost but negligible fixed cost; with the second supplier, the buyer incurs a lower variable cost but a positive fixed cost. At the same time, the ordering quantity is limited. We develop the optimal inventory control policy when the holding and shortage co...

The paper is devoted to variational analysis of set-valued mappings acting from quasimetric spaces into topological spaces with variable ordering structures. Besides the mathematical novelty, our motivation comes from applications to adaptive dynamical models of behavioral sciences. We develop a unified dynamical approach to variational principles in such settings based on the new minimal point...

Reversible logic synthesis is important for the design of conventional logic systems such as adiabatic logic and also for quantum logic systems since all quantum logic gates are necessarily reversible in nature. A framework is presented that improves reversible logic synthesis by employing a dynamically determined variable order for quantum multiple-valued decision diagrams (QMDD). We demonstra...

The MINCE heuristic for variable-ordering [1] can successfully reduce the size of BDDs and accelerate SAT-solving. Applications to reachability analysis have also been successful [12]. The main drawback of MINCE is its implementation complexity the authors used a pre-existing min-cut placer [6] that is several times larger than any existing SAT solver. Tweaking MINCE is difficult. In this work ...

| We present methods for the construction of small Ordered Kronecker Functional Decision Diagrams (OKFDDs). OKFDDs are a generalization of Ordered Binary Decision Diagrams (OBDDs) and Ordered Functional Decision Diagrams (OFDDs) as well. Starting with an upper bound for the size of an OKFDD representing a tree-like circuit we develope diierent heuristics to nd good variable orderings and decomp...