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A policy iteration algorithm for computing fixed points in static analysis of programs
- IN CAV
, 2005
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Nordic Journal of Computing An Incremental Unique Representation for Regular Trees
"... Abstract. In order to deal with infinite regular trees (or other pointed graph structures) efficiently, we give new algorithms to store such structures. The trees are stored in such a way that their representation is unique and shares substructures as much as possible. This maximal sharing allows su ..."
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Abstract. In order to deal with infinite regular trees (or other pointed graph structures) efficiently, we give new algorithms to store such structures. The trees are stored in such a way that their representation is unique and shares substructures as much as possible. This maximal sharing allows substantial memory gain and speed up over previous techniques. For example, equality testing becomes constant time (instead of O(n log(n))). The algorithms are incremental, and as such allow good reactive behavior. These new algorithms are then applied in a representation of sets of trees. The expressive power of this new representation is exactly what is needed by the original set-based analyses of Heintze and Jaffar [1990], or Heintze [1994]. CR Classification: See Computing Revues
Rapport n o RR-2010-022Functional Term Rewriting Systems
"... Abstract. This reseach report proposes the theoretical foundations of a new formal tool for symbolic verification of finite systems. Some approaches reduce the problem of system verification to the reachability problem in term rewriting systems (TRSs). In our approach, states are encoded by terms in ..."
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Abstract. This reseach report proposes the theoretical foundations of a new formal tool for symbolic verification of finite systems. Some approaches reduce the problem of system verification to the reachability problem in term rewriting systems (TRSs). In our approach, states are encoded by terms in a BDD-like manner and the transition relation is represented by a new rewriting relation so called Functional Term Rewriting Systems (FTRSs). First, we show that FTRSs are as expressive as TRSs. Then, we focus on a subclass of FTRSs, so called Elementary Functional Term Rewriting Systems (EFTRSs), and we show that EFTRSs preserve the FTRSs expressiveness. The main advantage of EFTRSs is that they are well adapted for acceleration techniques usually used in saturation algorithms on BDD-like data structures. Our experiments show that for well-known protocols (e.g. Tree Arbiter, Percolate, Round Robin Mutex protocols,...) our tool is not only better than other rewriting tools such as Timbuk or Maude, but also competitive with other model-checkers such as SPIN, NuSMV or SMART. Moreover, it can also be applied to model-checking invariant properties which are a particular subclass of linear temporal logic formula (LTL). 1
