M. BIEHL, N. KLARLUND, AND T. RAUHE, Mona: Decidable arithmetic in practice, in Proc. 4th International Symposium on Formal Techniques in RealTime and Fault-Tolerant Systems, FTRTFT '96, vol. 1135 of LNCS, SpringerVerlag, September 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for a very rich Duration Calculus [Pan00] is extremely high. While extreme, namely non elementary, complexity is in general unavoidable as deciding or model checking Duration Calculus is worst case non elementary [HZ97,Fr a02] this need not be the typical case, as the MONA experience shows [BKR96]. In fact, the author s ndings, when doing a prototype implementation of a Duration Calculus checker in 1996, were that considerably more ecient ad hoc constructions for typical speci cation formulae were easy to nd: However, the non elementary complexity of the decision procedure need not ....

....all models of length at most k. http: www.ee.princeton.edu chaff zchaff.php 0 20 40 60 80 100 120 140 0 1 2 3 4 5 6 DCValid BMC Fig. 2. Veri cation time for 2( 30 ) gas : ame n) Horizontal axis: n; vertical axis: time spent in veri cation backend (in seconds) [BKR96] in version 1.4 as a veri cation backend. All experiments were performed on a 500 MHz Pentium III M with 384 MByte RAM and 300 MByte swap space, running under Linux. In the sequel, we do just report the runtimes of the veri cation backends (i.e. ZCha and MONA) as a comparison of the translation ....

M. Biehl, N. Klarlund, and T. Rauhe. Mona: Decidable arithmetic in practice. In Jonsson and Parrow [JP96], pages 459-462.

....operations such as , 8, and multiplication by a constant can be defined as abbreviations to expressions in the basic syntax. It is possible to represent Presburger definable sets of integers using automata. Efficient translations to automata have been suggested in [WB95] BC96] WB00] MKR96] HJJ 96] Symbolic model checking has been done using Presburger arithmetic as the symbolic representation [BGP97] using ctl style temporal operators for specifications. The implementation uses the polyhedra based Omega library ] Pug92] which is a fast Presburger solver. The Omega library ....

Biehl Morten, Nils Klarlund, and Theis Rauhe. Mona: decidable arithmetic in practice. In Formal Techniques in Real-Time and Fault-Tolerant Systems, 4th International Symposium, Uppsala, LNCS 1135, 1996.

....model checkers in Sect. 5. Finally, we present our conclusions and future directions. 2 Related Work Another approach to infinite state model checking is to use automata based representations. Automata can be used to represent arithmetic constraints on unbounded integer variables [WB95,BKR96,KSA98] An arithmetic constraint on k integer variables is represented by a k track automata that accepts a string if it corresponds to a k dimensional integer vector (in binary representation) that satisfies the corresponding arithmetic constraint. Again, since the automata representation ....

M. Biehl, N. Klarlund, and T. Rauhe. Mona: Decidable arithmetic in practice. In Proceedings of Formal Techniques in Real-Time and Fault-Tolerant Systems, 4th International Symposium, volume 1135 of Lecture Notes in Computer Science. Springer, 1996.

....comparison within our framework. Does the implementation of Shasta reflect the true potential of the automata based approach Fortunately, we were able to answer this question to some degree by comparing Shasta directly to Mona, a second generation automata package that supports the logic WS1S [2, 14]. Rather than trying to integrate Mona into VIS, we just manually coded two examples (sdiv and euclid) in Mona s WS1S language, using the embedding suggested by Buchi. We also hardcoded the reachability computation out to a fixed number of steps for each example. By ensuring the same variable ....

M. Biehl, N. Klarlund, and T. Rauhe. Mona: Decidable arithmetic in practice. In B. Jonsson and J. Parrow, editors, Fourth International Symposium Formal Techniques in Real-Time and Fault-Tolerant Systems, volume 1135 of LNCS, Uppsala, Sweden, 1996. Springer-Verlag.

....QDD representation with BDD encoding [37] QBDDs have limited expressiveness for infinite sets. They are more appropriate for encoding bounded queues. The MONA tool is a library for manipulating automata based representations of formulas in WS1S (Weak Second order theory of One Successor) [8, 10, 41, 50]. WS1S corresponds to regular languages (languages accepted by finite automata) and subsumes a fragment of arithmetic (including Presburger arithmetic) The name MONA comes from monadic second order logic on finite strings, which can also be represented by the MONA tool using a different semantics ....

....a different semantics for the automata representation. The tool is based on some efficient algorithms for minimizing automata that uses BDDs to represent transition functions in compressed form. QBDD representation corresponds to a special case of the automata based representation used in MONA [10]. Several symbolic representations have been proposed for modeling functions over boolean variables with integer ranges, including Multi Terminal Binary Decision Diagrams (MTBDDs) 26] Binary Moment Diagrams (BMDs) 15] and their generalization Hybrid Decision Diagrams (HDDs) 26, 27] These are ....

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M. Biehl, N. Klarlund, and T. Rauhe. Mona: Decidable arithmetic in practice. In Proceedings of Formal Techniques in Real-Time and Fault-Tolerant Systems, 4th International Symposium, volume 1135 of Lecture Notes in Computer Science. Springer, 1996.

....Mona program, which consists of predicates (subroutines that are compiled separately) macros, and a main formula. Each back end implements the automatatheoretic operations that are carried out to decide the formula corresponding to the program. Since our earlier presentation of the Mona tool [1], we have completely rewritten the front end, this time in C (the earlier version was written in ML) In the old version, the front end produces a code tree, whose internal nodes each describe an automata theoretic operation such as a product or subset construction and whose leaves describe ....

M. Biehl, N. Klarlund, and T. Rauhe. Mona: decidable arithmetic in practice (short contribution). In Formal Techniques in Real-Time and Fault-Tolerant Systems, 4th International Symposium, LNCS 1135. Springer Verlag, 1996.

....logic is also decidable by the automaton logic connection, but using tree automata instead of string automata. The Mona tool also implements this decision procedure. There is a subtle di#erence between WS1S, the logic now used in Mona, and M2L Str, the logic used in early experimental versions [48, 6, 15]. The di#erence between WS2S and M2L Tree is similar. In WS1S, formulas are interpreted over infinite string models (but quantification is restricted to finite sets only) In M2LStr, formulas are instead interpreted over finite string models. That is, the universe is not the whole set of ....

Morten Biehl, Nils Klarlund, and Theis Rauhe. Mona: decidable arithmetic in practice (demo). In Formal Techniques in Real-Time and Fault-Tolerant Systems, 4th International Symposium, volume 1135 of LNCS, 1996.

....logic is also decidable by the automaton logic connection, but using tree automata instead of string automata. The Mona tool also implements this decision procedure. There is a subtle di erence between WS1S, the logic now used in Mona, and M2L Str, the logic used in early experimental versions [48, 6, 16]. The di erence between WS2S and M2L Tree is similar. In WS1S, formulas are interpreted over in nite string models (but quanti cation is restricted to nite sets only) In M2LStr, formulas are instead interpreted over nite string models. That is, the universe is not the whole set of naturals N, ....

Morten Biehl, Nils Klarlund, and Theis Rauhe. Mona: decidable arithmetic in practice (demo). In Formal Techniques in Real-Time and Fault-Tolerant Systems, 4th International Symposium, volume 1135 of LNCS, 1996.

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M. BIEHL, N. KLARLUND, AND T. RAUHE, Mona: Decidable arithmetic in practice, in Proc. 4th International Symposium on Formal Techniques in RealTime and Fault-Tolerant Systems, FTRTFT '96, vol. 1135 of LNCS, SpringerVerlag, September 1996.

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