Abstract. Knowledge compilation has been emerging recently as a new direction of research for dealing with the computational intractability of general propositional reasoning. According to this approach, the reasoning process is split into two phases: an off-line compilation phase and an online query-answering phase. In the off-line phase, the propositional theory is compiled into some target language, which is typically a tractable one. In the on-line phase, the compiled target is used to efficiently answer a (potentially) exponential number of queries. The main motivation behind knowledge compilation is to push as much of the computational overhead as possible into the offline phase, in order to amortize that overhead over all on-line queries. Another motivation behind compilation is to produce very simple on-line reasoning systems, which can be embedded costeffectively into primitive computational platforms, such as those found in consumer electronics. One of the key aspects of any compilation approach is the target language into which the propositional theory is compiled. Previous target languages included Horn theories, prime implicates/implicants and ordered binary decision diagrams (OBDDs). We propose in this paper a new target compilation language, known as decomposable negation normal form (DNNF), and present a number of its properties that make it of interest to the broad community. Specifically, we

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Implicit invocation or publish-subscribe has become an important architectural style for large-scale system design and evolution. The publish-subscribe style facilitates developing large-scale systems by composing separately developed components because the style permits loose coupling between various components. One of the major bottlenecks in using publish-subscribe systems for very large scale systems is the efficiency of filtering incoming messages, i.e., matching of published events with event subscriptions. This is a very challenging problem because in a realistic publishsubscribe system the number of subscriptions can be large. In this paper we present an approach for matching published events with subscriptions which scales to a large number of subscriptions. Our approach uses Binary Decision Diagrams, a compact data structure for representing boolean functions which has been successfully used in verification techniques such as model checking. Experimental results clearly demonstrate the efficiency of our approach.

We compare two prominent decision procedures for propositional logic: Ordered Binary Decision Diagrams (obdds) and the DavisPutnam procedure. Experimental results indicate that the Davis-Putnam procedure outperforms obdds in hard constraint-satisfaction problems, while obdds are clearly superior for Boolean functional equivalence problems from the circuit domain, and, in general, problems that require the schematization of a large number of solutions that share a common structure. The two methods illustrate the different and often complementary strengths of constraint-oriented and search-oriented procedures.

. The use of a lower bound estimate in the search has a tremendous impact on the size of the resulting search trees, whereas OBDDs can be used to efficiently describe sets of states based on their binary encoding. This paper combines these two ideas into a new algorithm BDDA . It challenges both the breadth-first search using OBDDs and the traditional A algorithm. The problem with A is that in many application areas the set of states is too huge to be kept in main memory. In contrast, brute-force breadth-first search using OBDDs unnecessarily expands several nodes. Therefore, we exhibit a new trade-off between time and space requirements and tackle the most important problem in heuristic search, the overcoming of space limitations while avoiding a strong penalty in time. We evaluate our approach in the (n 2 \Gamma 1)-Puzzle and within Sokoban. 1 Introduction In heuristic search we explore the state space by generating the successor set over and over again. The choice...

OBDD's are the state-of-the-art data structure for Boolean function manipulation since basic tasks of Boolean manipulation such as testing equivalence, satisfiability, or tautology, and performing single Boolean synthesis steps can be done efficiently. In the following we show that the efficient manipulation of OBDD's can be extended to a more general data structure, so-called FBDD's. In detail, the advantages of using FBDD's instead of OBDD's are ffl FBDD's are generally more (sometimes even exponentially more) succinct than OBDD's, ffl FBDD's provide, similarly to OBDD's, canonical representations of Boolean functions, and ffl in terms of FBDD's basic tasks of Boolean manipulation can be performed similarly efficient as in terms of OBDD's. The power of the FBDD-concept is demonstrated by showing that the verification of the benchmark circuit design for the hidden weighted bit function HWB proposed by Bryant can be carried out efficiently in terms of FBDD's while, for princip...

Many researchers have reported that the use of Boolean decision diagrams (BDDs) greatly increases the size of hardwaredesigns that can be formally verifiedautomatically. Our own experience with automatic verification of high-level aspects of hardware design, such as protocols for cache coherence and communications, contradicts previous results; in fact, BDDs have been substantially inferior to brute-force algorithms that store states explicitly in a table. We believe that new techniques will be needed to realize the potential advantages of BDD verification at the protocol level. Here, we identify functionally dependent variables as a common cause of BDD-size blowup, and describe new techniques to avoid the problem. Using the improved algorithm, we reduce an exponentiallysized problem to a provably O(n log n)-sized one, achieving several orders of magnitude reduction in BDD size. I INTRODUCTION With the increasing cost and complexity of hardware designs and protocols, formal verificatio...

. We prove that read-once branching programs computing integer multiplication require size 2 ## # n) . This is the first nontrivial lower bound for multiplication on branching programs that are not oblivious. By the appropriate problem reductions, we obtain the same lower bound for other arithmetic functions. Key words. multiplication, read-once, branching programs, BDD, verification AMS subject classifications. 68Q05, 68Q25, 68M15 PII. S0097539795290349 1. Introduction and background. It is well known that many functions, some of them very simple, cannot be computed by read-once branching programs of polynomial size [We88, Za84, Du85, We87, BHST87, Ju88, Kr88]. Interest in whether integer multiplication can be so computed has been created by recent developments in the field of digital design and hardware verification. 1.1. Hardware verification and branching programs. The central problem of verification is to check whether a combinational hardware circuit has been correctly designe...

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. We consider a variant of the Boolean satisfiability problem where a subset E of the propositional variables appearing in formula F sat encode a symmetric, transitive, binary relation over N elements. Each of these relational variables, e i;j , for 1 i ! j N , expresses whether or not the relation holds between elements i and j. The task is to either find a satisfying assignment to F sat that also satisfies all transitivity constraints over the relational variables (e.g., e1;2 e2;3 ) e1;3 ), or to prove that no such assignment exists. Solving this satisfiability problem is the final and most difficult step in our decision procedure for a logic of equality with uninterpreted functions. This procedure forms the core of our tool for verifying pipelined microprocessors. To use a conventional Boolean satisfiability checker, we augment the set of clauses expressing F sat with clauses expressing the transitivity constraints. We consider methods to reduce the number of such cla...