Binary Decision Diagrams (BDDs) are instrumental in many electronic design automation (EDA) tasks thanks to their compact representation of Boolean functions. In BDD-based reversible-circuit synthesis, which is critical for quantum computing, the chosen variable ordering governs the number of BDD nodes and thus the key metrics of resource consumption, such as Quantum Cost. Because finding an optimal variable ordering for BDDs is an NP-complete problem, existing heuristics often degrade as circuit complexity grows. We introduce BDD2Seq, a graph-to-sequence framework that couples a Graph Neural Network encoder with a Pointer-Network decoder and Diverse Beam Search to predict high-quality orderings. By treating the circuit netlist as a graph, BDD2Seq learns structural dependencies that conventional heuristics overlooked, yielding smaller BDDs and faster synthesis. Extensive experiments on three public benchmarks show that BDD2Seq achieves around 1.4 times lower Quantum Cost and 3.7 times faster synthesis than modern heuristic algorithms. To the best of our knowledge, this is the first work to tackle the variable-ordering problem in BDD-based reversible-circuit synthesis with a graph-based generative model and diversity-promoting decoding.

While the game Connect-Four has been solved mathematically and the best move can be effectively computed with search based methods, a strong solution in the form of a look-up table was believed to be infeasible. In this paper, we revisit a symbolic search method based on binary decision diagrams to produce strong solutions. With our efficient implementation we were able to produce a 89.6 GB large look-up table in 47 hours on a single CPU core with 128 GB main memory for the standard $7 \times 6$ board size. In addition to this win-draw-loss evaluation, we include an alpha-beta search in our open source artifact to find the move which achieves the fastest win or slowest loss.

In multicriteria decision-making, a user seeks a set of non-dominated solutions to a (constrained) multiobjective optimization problem, the so-called Pareto frontier. In this work, we seek to bring a state-of-the-art method for exact multiobjective integer linear programming into the heuristic realm. We focus on binary decision diagrams (BDDs) which first construct a graph that represents all feasible solutions to the problem and then traverse the graph to extract the Pareto frontier. Because the Pareto frontier may be exponentially large, enumerating it over the BDD can be time-consuming. We explore how restricted BDDs, which have already been shown to be effective as heuristics for single-objective problems, can be adapted to multiobjective optimization through the use of machine learning (ML). MORBDD, our ML-based BDD sparsifier, first trains a binary classifier to eliminate BDD nodes that are unlikely to contribute to Pareto solutions, then post-processes the sparse BDD to ensure its connectivity via optimization. Experimental results on multiobjective knapsack problems show that MORBDD is highly effective at producing very small restricted BDDs with excellent approximation quality, outperforming width-limited restricted BDDs and the well-known evolutionary algorithm NSGA-II.

We propose a query learning algorithm for ordered multi-terminal binary decision diagrams (OMTBDDs) using at most n equivalence and 2n(l\lcei\log_2 m\rceil+ 3n) membership queries by extending the algorithm for ordered binary decision diagrams (OBDDs). Tightness of our upper bounds is checked in our experiments using synthetically generated target OMTBDDs. Possibility of applying our algorithm to classification problems is also indicated in our other experiments using datasets of UCI Machine Learning Repository.

In many settings (e.g., robotics) demonstrations provide a natural way to specify sub-tasks; however, most methods for learning from demonstrations either do not provide guarantees that the artifacts learned for the sub-tasks can be safely composed and/or do not explicitly capture history dependencies. Motivated by this deficit, recent works have proposed specializing to task specifications, a class of Boolean non-Markovian rewards which admit well-defined composition and explicitly handle historical dependencies. This work continues this line of research by adapting maximum causal entropy inverse reinforcement learning to estimate the posteriori probability of a specification given a multi-set of demonstrations. The key algorithmic insight is to leverage the extensive literature and tooling on reduced ordered binary decision diagrams to efficiently encode a time unrolled Markov Decision Process.

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 the Boolean variables. Finding the optimal variable order has been proved a NP-complete problem. Many heuristics have been proposed to find a near-optimal solution of this problem. In this paper, we propose a neural network-based method to predict near-optimal variable orders for unknown formulas. Viewing these formulas as hypergraphs, and lifting the message passing neural network into 3-hypergraph (MPNN3), we are able to learn the patterns of Boolean formula. Compared to the traditional methods, our method can find a near-the-best solution with an extremely shorter time, even for some hard examples.To the best of our knowledge, this is the first work on applying neural network to OBDD reordering.

In the past, BDDs have significantly improved the performance of algorithms and enabled the solution of new classes of problems in areas such as formal verification and logic synthesis (see, for example, Burch et al. [1992]). Surprisingly, BDDs have only recently been introduced to implement the solution of planning problems (Cimatti et al. 1997). The goal of our project was to investigate whether BDDs might also help to increase the efficiency of algorithms solving problems in the field of reasoning about action and change. For a start, I have implemented the solution of fluent calculus planning problems restricted to deterministic actions and propositional fluents (Hölldobler and Störr 2000; Störr 2001). The idea of BDDs is similar to decision trees: A Boolean function is represented as a rooted acyclic-directed graph.

FF. Readers interested in these The 1 sink can only be reached by following the edges labeled 1 from A and B; thus, the represented Boolean function (A, B) evaluates to true if and only if A and B are true. The characteristic function can be identified with the set itself. It seems worthwhile to spend some effort on finding a "good" encoding, which is where the preprocessing of The corresponding BDDs are illustrated in figure 2. Bin We were able to reformulate the initial and final situations as BDDs. As an end in itself, this representation does not help too much. We are interested in a sequence of actions (or transitions) that transforms an initial state into one that satisfies the goal condition.

Selman and Kautz's work on ``knowledge compilation'' established how approximation (strengthening and/or weakening) of a propositional knowledge-base can be used to speed up query processing, at the expense of completeness. In this classical approach, querying uses Horn over- and under-approximations of a given knowledge-base, which is represented as a propositional formula in conjunctive normal form (CNF). Along with the class of Horn functions, one could imagine other Boolean function classes that might serve the same purpose, owing to attractive deduction-computational properties similar to those of the Horn functions. Indeed, Zanuttini has suggested that the class of affine Boolean functions could be useful in knowledge compilation and has presented an affine approximation algorithm. Since CNF is awkward for presenting affine functions, Zanuttini considers both a sets-of-models representation and the use of modulo 2 congruence equations. In this paper, we propose an algorithm based on reduced ordered binary decision diagrams (ROBDDs). This leads to a representation which is more compact than the sets of models and, once we have established some useful properties of affine Boolean functions, a more efficient algorithm.

The size and complexity of software and hardware systems have significantly increased in the past years. As a result, it is harder to guarantee their correct behavior. One of the most successful methods for automated verification of finite-state systems is model checking. Most of the current model-checking systems use binary decision diagrams (BDDs) for the representation of the tested model and in the verification process of its properties. Generally, BDDs allow a canonical compact representation of a boolean function (given an order of its variables). The more compact the BDD is, the better performance one gets from the verifier. However, finding an optimal order for a BDD is an NP-complete problem. Therefore, several heuristic methods based on expert knowledge have been developed for variable ordering. We propose an alternative approach in which the variable ordering algorithm gains 'ordering experience' from training models and uses the learned knowledge for finding good orders. Our methodology is based on offline learning of pair precedence classifiers from training models, that is, learning which variable pair permutation is more likely to lead to a good order. For each training model, a number of training sequences are evaluated. Every training model variable pair permutation is then tagged based on its performance on the evaluated orders. The tagged permutations are then passed through a feature extractor and are given as examples to a classifier creation algorithm. Given a model for which an order is requested, the ordering algorithm consults each precedence classifier and constructs a pair precedence table which is used to create the order. Our algorithm was integrated with SMV, which is one of the most widely used verification systems. Preliminary empirical evaluation of our methodology, using real benchmark models, shows performance that is better than random ordering and is competitive with existing algorithms that use expert knowledge. We believe that in sub-domains of models (alu, caches, etc.) our system will prove even more valuable. This is because it features the ability to learn sub-domain knowledge, something that no other ordering algorithm does.