Chain Reduction for Binary and Zero-Suppressed Decision Diagrams

Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others' ability to symbolically represent Boolean functions in compact form. For any Boolean function, its chain-reduced ZDD (CZDD) representation will be no larger than its ZDD representation, and at most twice the size of its BDD representation. The chain-reduced BDD (CBDD) of a function will be no larger than its BDD representation, and at most three times the size of its CZDD representation. Extensions to the standard algorithms for operating on BDDs and ZDDs enable them to operate on the chain-reduced versions. Experimental evaluations on representative benchmarks for encoding word lists, solving combinatorial problems, and operating on digital circuits indicate that chain reduction can provide significant benefits in terms of both memory and execution time

Lex-Partitioning: A New Option for BDD Search

For the exploration of large state spaces, symbolic search using binary decision diagrams (BDDs) can save huge amounts of memory and computation time. State sets are represented and modified by accessing and manipulating their characteristic functions. BDD partitioning is used to compute the image as the disjunction of smaller subimages. In this paper, we propose a novel BDD partitioning option. The partitioning is lexicographical in the binary representation of the states contained in the set that is represented by a BDD and uniform with respect to the number of states represented. The motivation of controlling the state set sizes in the partitioning is to eventually bridge the gap between explicit and symbolic search. Let n be the size of the binary state vector. We propose an O(n) ranking and unranking scheme that supports negated edges and operates on top of precomputed satcount values. For the uniform split of a BDD, we then use unranking to provide paths along which we partition the BDDs. In a shared BDD representation the efforts are O(n). The algorithms are fully integrated in the CUDD library and evaluated in strongly solving general game playing benchmarks.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611

Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial

Petri net analysis using boolean manipulation

This paper presents a novel analysis approach for bounded Petri nets. The net behavior is modeled by boolean functions, thus reducing reasoning about Petri nets to boolean calculation. The state explosion problem is managed by using Binary Decision Diagrams (BDDs), which are capable to represent large sets of markings in small data structures. The ability of Petri nets to model systems, the flexibility and generality of boolean algebras, and the efficient implementation of BDDs, provide a general environment to handle a large variety of problems. Examples are presented that show how all the reachable states (1018) of a Petri net can be efficiently calculated and represented with a small BDD (103 nodes). Properties requiring an exhaustive analysis of the state space can be verified in polynomial time in the size of the BDD.Peer ReviewedPostprint (author's final draft

Efficient parallel binary decision diagram construction using Cilk

Thesis (S.B. and M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.Includes bibliographical references (leaves 44-45).by David B. Berman.S.B.and M.Eng

Symbolic Implementation of Connectors in BIP

BIP is a component framework for constructing systems by superposing three layers of modeling: Behavior, Interaction, and Priority. Behavior is represented by labeled transition systems communicating through ports. Interactions are sets of ports. A synchronization between components is possible through the interactions specified by a set of connectors. When several interactions are possible, priorities allow to restrict the non-determinism by choosing an interaction, which is maximal according to some given strict partial order. The BIP component framework has been implemented in a language and a tool-set. The execution of a BIP program is driven by a dedicated engine, which has access to the set of connectors and priority model of the program. A key performance issue is the computation of the set of possible interactions of the BIP program from a given state. Currently, the choice of the interaction to be executed involves a costly exploration of enumerative representations for connectors. This leads to a considerable overhead in execution times. In this paper, we propose a symbolic implementation of the execution model of BIP, which drastically reduces this overhead. The symbolic implementation is based on computing boolean representation for components, connectors, and priorities with an existing BDD package

Fast Parallel Deterministic and Randomized Algorithms for Model Checking

Model checking is a powerful technique for verification of concurrent systems. One of the potential problems with this technique is state space explosion. There are two ways in which one could cope with state explosion: reducing the search space and searching less space. Most of the existing algorithms are based on the first approach. One of the successful approach for reducing search space uses Binary Decision Diagrams (BDDs) to represent the system. Systems with a large number of states (of the order of 5 x 10 ) have been thus verified. But there are limitations to this heuristic approach. Even systems of reasonable complexity have many more states. Also, the BDD approach might fail even on some simple systems. In this paper we propose the use of parallelism to extend the applicability of BDDs in model checking. In particular we present very fast algorithms for model checking that employ BDDs. The algorithms presented are much faster than the best known previous algorithms. We also describe searching less space as an attractive approach to model checking. In this paper we demonstrate the power of this approach. We also suggest the use of randomization in the design of model checking algorithms

Multi-core Decision Diagrams

Decision diagrams are fundamental data structures that revolutionized fields such as model checking, automated reasoning and decision processes. As performance gains in the current era mostly come from parallel processing, an ongoing challenge is to develop data structures and algorithms for modern multicore architectures. This chapter describes the parallelization of decision diagram operations as implemented in the parallel decision diagram package Sylvan, which allows sequential algorithms that use decision diagrams to exploit the power of multi-core machines