JINC - A Multi-Threaded Library for Higher-Order Weighted Decision Diagram Manipulation

Ordered Binary Decision Diagrams (OBDDs) have been proven to be an efficient data structure for symbolic algorithms. The efficiency of the symbolic methods de- pends on the underlying OBDD library. Available OBDD libraries are based on the standard concepts and so far only differ in implementation details. This thesis introduces new techniques to increase run-time and space-efficiency of an OBDD library. This thesis introduces the framework of Higher-Order Weighted Decision Diagrams (HOWDDs) to combine the similarities of different OBDD variants. This frame- work pioneers the basis for the new variant Toggling Algebraic Decision Diagrams (TADDs) which has been shown to be a space-efficient HOWDD variant for sym- bolic matrix representation. The concept of HOWDDs has been use to implement the OBDD library JINC. This thesis also analyzes the usage of multi-threading techniques to speed-up OBDD manipulations. A new reordering framework ap- plies the advantages of multi-threading techniques to reordering algorithms. This approach uses an abstraction layer so that the original reordering algorithms are not touched. The challenge that arise from a straight forward algorithm is that the computed-tables and the garbage collection are not as efficient as in a single- threaded environment. We resolve this problem by developing a new multi-operand APPLY algorithm that eliminates the creation of temporary nodes which could occur during computation and thus reduces the need for caching or garbage collection. The HOWDD framework leads to an efficient library design which has been shown to be more efficient than the established OBDD library CUDD. The HOWDD instance TADD reduces the needed number of nodes by factor two compared to ordinary ADDs. The new multi-threading approaches are more efficient than single-threading approaches by several factors. In the case of the new reordering framework the speed- up almost equals the theoretical optimal speed-up. The novel multi-operand APPLY algorithm reduces the memory usage for the n-queens problem by factor 50 which enables the calculation of bigger problem instances compared to the traditional APPLY approach. The new approaches improve the performance and reduce the memory footprint. This leads to the conclusion that applications should be reviewed whether they could benefit from the new multi-threading multi-operand approaches introduced and discussed in this thesis

Dynamic Minimization of Word-Level Decision Diagrams

Word-Level Decision Diagrams (WLDDs), like *BMDs and K*BMDs, have recently been introduced as a data structure for verification. The size of WLDDs largely depends on the chosen variable ordering, i.e. the ordering in which variables are encountered, and on the decompositions carried out in each node. In this paper we present a framework for dynamic minimization of WLDDs. We discuss the difficulties with previous techniques if applied to WLDDs and present a new approach that efficiently adapts both variable ordering and decomposition type choice. Experimental results demonstrate that this method outperforms "classical" reordering with respect to runtime and representation size during dynamic minimization of word-level functions. 1 Introduction Most formal approaches in verification nowadays make use of function representation by Decision Diagrams (DDs). In this context Ordered Binary Decision Diagrams (OBDDs) [5] have intensively been studied and frequently applied. Unfortunately, OB..