Related papers: On an optimization technique using Binary Decision…
For three decades binary decision diagrams, a data structure efficiently representing Boolean functions, have been widely used in many distinct contexts like model verification, machine learning, cryptography and also resolution of…
This paper proposes a new logic optimization paradigm based on circuit simulation, which reduces the need for Boolean computations such as SAT-solving or constructing BDDs. The paper develops a Boolean resubstitution framework to…
This paper presents algorithms for the included-sums and excluded-sums problems used by scientific computing applications such as the fast multipole method. These problems are defined in terms of a $d$-dimensional array of $N$ elements and…
Safety-critical controllers of complex systems are hard to construct manually. Automated approaches such as controller synthesis or learning provide a tempting alternative but usually lack explainability. To this end, learning decision…
A number of problems in relational Artificial Intelligence can be viewed as Stochastic Constraint Optimization Problems (SCOPs). These are constraint optimization problems that involve objectives or constraints with a stochastic component.…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision…
Decision Diagrams (DDs) have emerged as a powerful tool for discrete optimization, with rapidly growing adoption. DDs are directed acyclic layered graphs; restricted DDs are a generalized greedy heuristic for finding feasible solutions, and…
The growing interest in explainable artificial intelligence (XAI) for critical decision making motivates the need for interpretable machine learning (ML) models. In fact, due to their structure (especially with small sizes), these models…
Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their…
Automatic industrial scheduling, aiming at optimizing the sequence of jobs over limited resources, is widely needed in manufacturing industries. However, existing scheduling systems heavily rely on heuristic algorithms, which either…
Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision…
Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…
Sentential decision diagrams (SDDs) introduced by Darwiche in 2011 are a promising representation type used in knowledge compilation. The relative succinctness of representation types is an important subject in this area. The aim of the…
The sum-product algorithm for decoding of binary codes is analyzed for bipartite graphs in which the check nodes all have degree $2$. The algorithm simplifies dramatically and may be expressed using linear algebra. Exact results about the…
The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery…
Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query…
A binary string of length $2^k$ induces the Boolean function of $k$ variables whose Shannon expansion is the given binary string. This Boolean function then is representable via a unique reduced ordered binary decision diagram (ROBDD). The…
Ordered binary decision diagrams (OBDDs) are an efficient data structure for representing and manipulating Boolean formulas. With respect to different variable orders, the OBDDs' sizes may vary from linear to exponential in the number of…
Markov decisions processes (MDPs) are becoming increasing popular as models of decision theoretic planning. While traditional dynamic programming methods perform well for problems with small state spaces, structured methods are needed for…