B. Bloom and R. Paige. Transformational Design and Implementation of a New E#cient Solution to the Ready Simulation Problem, Science of Computer Programming 24(1995), pp. 189--220.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the workshop SAVE 2001. Email: gentilin dimi.uniud.it Email: piazza dimi.uniud.it Email: policrit dimi.uniud.it c #2002 Published by Elsevier Science B. V. and O( E ) steps, respectively. A simulation procedure having a time complexity of O( N E ) was independently defined in [2] and in [12] The space required by each of the above mentioned routines is limited from below by . Recently [6] 3] and [10] improved the space complexity of the problem which is an extremely significant parameter in the context of verification. In particular, the procedure in [6] ....

....Equivalence] Given G = E, ##, the maximum simulation equivalence N is defined as: n s n. Lemma 2.5 The relation s is an equivalence relation. We consider the problem of computing s over G = E, ##. All of the algorithms mentioned in the introduction ( 1] 4] 5] [2], 12] obtain the similarity quotient, S = N s , as a by product of the computation of the similarity relation on N . Their space complexity is then limited from below by O( N ) The simulation algorithms in [6] 3] and [10] do not compute the entire simulation relation over N and hence ....

Bard Bloom and Robert Paige. Transformational design and implementation of a new e#cient solution to the ready simulation problem. Science of Computer Programming, 24(3):189--220, June 1995.

....for computing the simulation ordering underpin algorithms for computing relations such as trace inclusion and the failures must preorder [CH93] Despite its utility, not much attention has been paid to algorithms for computing the simulation ordering for nite state systems. Bloom and Paige [BP95] present a global routine that runs in time O(m 1 n 2 m 2 n 1 ) where m i and n i represent the number of states and transitions in the two systems being checked. Essentially the same algorithm was discovered independently in [HHK95] and similar ideas may be found in [CC95,CS90] Celikkan ....

....was discovered independently in [HHK95] and similar ideas may be found in [CC95,CS90] Celikkan [Cel95] de nes an on the y algorithm of comparable complexity. This paper develops a new technique for computing the simulation ordering that combines the xpoint calculation techniques of [BP95] with the fast bisimulation minimization algorithm due to Paige and Tarjan [PT87,Fer90] One well known way to improve the performance of a simulation checker is rst to minimize the systems in question with respect to bisimulation in order to reduce the number of states that must be considered. ....

[Article contains additional citation context not shown here]

B. Bloom and R. Paige. Transformational design and implementation of a new ecient solution to the ready simulation problem. Science of Computer Programming, 24(3):189-220, June 1995.

....per Chapter 7. Bisimulation checker used in CWB NC is a modified Paige Tarjan [40] adapted to compute # bisimulation: it starts with a partition induced by an equivalence relation #, instead of the trivial partition. The simulation relation is computed by a variant of the Bloom Paige algorithm [5]. Model Checking For reasons of e#ciency, the CWB NC has implemented more than one model checker, each of which is tailored for certain fragment of calculus. The current release of CWB NC includes a linear algorithm for the alternation free fragment [14] and a L2 model checker [3] The CWB NC ....

....of splitting. The algorithm has the same time complexity as Paige Tarjan algorithm when used to compute bisimulation. In our experiment, this checker has the same speed as Paige Tarjan algorithm in computing bisimulation relation. It preforms considerably better than the Bloom Paige algorithm [5] when computing simulation. In Chapter 9 we discussed how to adapt the naive algorithm to use KA PRTs as its internal representation of partitions. In our implementation, we use the exactly same idea to implement the three way splitting algorithm for the KA partition problem. Therefore, extracting ....

B. Bloom and R. Paige. Transformational design and implementation of a new e#cient solution to the ready simulation problem. Science of Computer Programming, 24(3):189--220, 1995.

....of algorithms from speci cations by program transformation. Already in the mid eighties, Bob was way ahead of the pack: instead of applying transformational techniques to well worn examples, he was applying his theories of program transformation to new problems, and discovering new algorithms [16, 48, 52]. The secret of his success lay partly in his insistence on the study of general algorithm design strategies (in particular nite di erencing [47, 51] and data structure selection [19] rather than the study of tiny derivational steps that some of the working group had focussed on. His success in ....

....turned out to be so pretty that we decided to include it in this paper. It would be interesting to see a further exploration of automata and language theory in this style (see also [5, 13, 53] The application of program transformation to algorithms involving automata was pioneered by Bob Paige [16, 22, 39]. Very recently we became aware that existential regular path queries are a well studied subject in the database community. In particular, the query language UnQL provides the possibility of querying hierarchically structured data through the use of regular expressions that contain variables ....

B. Bloom and R. Paige. Transformational design and implementation of a new e- cient solution to the ready simulation problem. Science of Computer Programming, 24(3):189-220, 1995.

....Ready trace equivalence Failures trace equivalence Failures equivalence Completed trace equivalence Trace equivalence Figure 1: The linear time branching time hierarchy of equivalences. several researchers have studied the decision problems for these relations [KS90, PT87, HT94, SRHS96, BP94, And93, And94, ABGS91, CS91, MS95, Hut91, HT90] A main distinction has turned out to be that of finite state processes versus infinite state processes. It is well known that all behavioural relations in the van Glabbeek hierarchy are decidable for finite state processes, and the main concern is ....

....partition refinement strategy using an algorithm due to Paige and Tarjan. The polynomial time algorithms for simulation equivalence and ready simulation equivalence by Huynh and Tian [HT94] employs a different strategy for computing the largest fixed point. The Bloom and Paige algorithm in [BP94] for ready simulation uses yet another variant of the approximation approach. 3.3.2 Characteristic formulae Another approach to equivalence checking appeals to model checking by constructing characteristic formulae. Following Hennessy and Milner [HM85] properties of labelled transition ....

B. Bloom and R. Paige, Transformational design and implementation of a new efficient solution to the ready simulation problem, Draft (1994). 30

....similarity quotients have been proposed: the ones presented in [2] 6] and [7] achieve time complexities of the orders O(jN j 6 jEj) O(jN j 4 jEj) and O(jEj 2 ) respectively. The best time complexity for algorithms computing the maximal simulation is the one presented in [11] and [3]: O(jN jjEj) All of the algorithms just mentioned ( 2] 6] 7] 3] 11] obtain the similarity quotient as a by product of the computation of the similarity relation on the set of states N . Their space complexity is then limited from below by O(jN j 2 ) Recently Bustan and Grumberg ....

....[6] and [7] achieve time complexities of the orders O(jN j 6 jEj) O(jN j 4 jEj) and O(jEj 2 ) respectively. The best time complexity for algorithms computing the maximal simulation is the one presented in [11] and [3] O(jN jjEj) All of the algorithms just mentioned ( 2] 6] 7] [3], 11] obtain the similarity quotient as a by product of the computation of the similarity relation on the set of states N . Their space complexity is then limited from below by O(jN j 2 ) Recently Bustan and Grumberg proposed an algorithm which gives in output the quotient structure with ....

[Article contains additional citation context not shown here]

Bard Bloom and Robert Paige. Transformational design and implementation of a new ecient solution to the ready simulation problem. Science of Computer Programming, 24(3):189-220, June 1995.

....of algorithms from speci cations by program transformation. Already in the mid eighties, Bob was way ahead of the pack: instead of applying transformational techniques to well worn examples, he was applying his theories of program transformation to new problems, and discovering new algorithms [17, 49, 53]. The secret of his success lay partly in his insistence on the study of general algorithm design strategies (in particular nite di erencing [48, 52] and data structure selection [20] rather than the study of tiny derivational steps that some of the working group had focussed on. His success in ....

....turned out to be so pretty that we decided to include it in this paper. It would be interesting to see a further exploration of automata and language theory in this style (see also [5, 14, 54] The application of program transformation to algorithms involving automata was pioneered by Bob Paige [17, 23, 40]. Very recently we became aware that existential regular path queries are a well studied subject in the database community. In particular, the query language UnQL provides the possibility of querying hierarchically structured data through the use of regular expressions that contain variables ....

B. Bloom and R. Paige. Transformational design and implementation of a new e- cient solution to the ready simulation problem. Science of Computer Programming, 24(3):189-220, 1995.

....can dispense with algorithms for computing ordinary and direct simulation right away, matching the best known upper bounds: with one priority the winning set for Zero can be determined by a variant of AND OR graph accessibility, computable in linear time (see, e.g. And94] Thus: Corollary 1. [HHK95,BP95]) Given a Buchi automaton A, with n states and m transitions, both o and di can be computed in time O(mn) 3.2 Bisimulation bisimulations can also be reformulated as parity games. For improving the complexity, such a reformulation only helps for fair bisimulation. Ordinary and direct ....

B. Bloom and R. Paige. Transformational design and implementation of a new efficient solution to the ready simulation problem. Science of Computer Programming, 24(3):189--220, 1995.

....similarity quotients have been proposed: the ones presented in [1] 4] and [5] achieve time complexities of the orders O(jN j 6 jEj) O(jN j 4 jEj) and O(jEj 2 ) respectively. The best time complexity for algorithms computing the maximal simulation is the one presented in [9] and [2] (O(jN jjEj) An (slow) algorithm improving the space complexity of the problem (an extremely signi cant parameter in the context of veri cation) is [3] In [8] an algorithm faster than [3] and improving on the space complexity of [9] is proposed. Our approach to the problem of simulation ....

....equivalence s is de ned as n s m , n s m m s n: Lemma 5 Given a graph G the maximum simulation equivalence s over G is an equivalence relation. 2 Given a graph G, we consider the problem of computing s . All of the algorithms mentioned in the introduction ( 1] 4] 5] [2], 9] obtain the similarity quotient as a by product of the computation of the similarity relation on the set of states N . Their space complexity is then limited from below by O(jN j 2 ) Recently Bustan and Grumberg proposed an algorithm which gives in output the quotient structure with ....

[Article contains additional citation context not shown here]

Bard Bloom and Robert Paige. Transformational design and implementation of a new ecient solution to the ready simulation problem. Science of Computer Programming, 24(3):189-220, June 1995.

.... [41, 39] and real time simulation [40, 9] Formal algorithm description and derivation allow us to obtain not only a more ecient algorithm but also more accurate complexity compared to previous work [29] Previously, this method has been applied to a number of other nontrivial problems, e.g. [7, 26]. At the center of the method is incremental computation of expensive set expressions by nite di erencing, where maintaining expensive subexpressions (E1 to E4 and W ) and auxiliary expressions (E11 to E41) in additional to the desired output (O) is crucial for achieving the eciency of the ....

B. Bloom and R. Paige. Transformational design and implementation of a new ecient solution to the ready simulation problem. Sci. Comput. Program., 24(3):189-220, 1995.

....contains no two items with the same value. Each item contained in a set can thus be indexed by its value. The size of a set is the number of items contained in the set. For example: SETL a = SET OF(1,TRUE, C ,TRUE) a set of 3 items SETL b = SET(1,3,10) a set of 5 odd integers within [1,10] Maps. A map is a set that contains only pairs (i.e. tuples of size of 2) Maps are special in the sense they can be used as functions (see Section 2.4) A pair in a map specifies a 1. Omega is denoted as OM in LIBSETL Key Features 4 of 18 An Advanced C Library for Symbolic Computing mapping ....

....of 18 An Advanced C Library for Symbolic Computing 5 Applications Many applications exist for LIBSETL. This section briefly enumerates a few key areas to which the library can be readily applied. All of the following discussions are based on an algorithmic example presented by Bloom and Paige[1], which provides an efficient solution to the ready simulation problem. The first page of the appendix shows the original algorithm in SETL and the second page shows its corresponding C version using LIBSETL. 5.1 C Programming in a Symbolic Style One of the primary applications of LIBSETL is ....

B. Bloom and R. Paige, "Transformational Design and Implementation Of A New Efficient Solution To The Ready Simulation Problem", Science of Computer Programming, 24(3), 1995.

....of algorithms from speci cations by program transformation. Already in the mid eighties, Bob was way ahead of the pack: instead of applying transformational techniques to well worn examples, he was applying his theories of program transformation to new problems, and discovering new algorithms [17, 49, 53]. The secret of his success lay partly in his insistence on the study of general algorithm design strategies (in particular nite di erencing [48, 52] and data structure selection [20] rather than the study of tiny derivational steps that some of the working group had focussed on. His success in ....

....out to be so pretty that we decided to include it in this paper. It would be interesting to see a further exploration of automata and language theory in this style 17 (see also [5, 14, 54] The application of program transformation to algorithms involving automata was pioneered by Bob Paige [17, 23, 40]. Very recently we became aware that existential regular path queries are a well studied subject in the database community. In particular, the query language UnQL provides the possibility of querying hierarchically structured data through the use of regular expressions that contain variables ....

B. Bloom and R. Paige. Transformational design and implementation of a new e- cient solution to the ready simulation problem. Science of Computer Programming, 24(3):189-220, 1995.

.... the copying of aggregates, in his purely functional programming language, EAS, a packaging of the typed calculus as extended with homogeneous sets [210, 211, 212] Transformational programming can be regarded as a formalization of Dijkstra s stepwise refinement [57, 58] As Bloom and Paige [28] point out, the transformational methodology is able to do much more than merely optimize code, or translate a SETLlike language into a C like one. By helping the algorithm designer reason about time and space complexity in syntactic terms rather than only by means of low level counting arguments, ....

.... designer reason about time and space complexity in syntactic terms rather than only by means of low level counting arguments, this technology has actually played a significant role in the invention of several new algorithms with greatly reduced asymptotic complexity compared to previous solutions [165, 163, 32, 31, 28, 34, 38, 93], while it has rendered the algorithms themselves more perspicuous both to their inventors and to their students. The next phase in the development of APTS will seek to improve both its reliability and its performance. Currently, all program transformations in APTS are proved correct ....

Bard Bloom and Robert Paige. Transformational design and implementation of a new efficient solution to the ready simulation problem. Science of Computer Programming, 24(3):189--220, 1995.

....Kripke structure does not change, thus all three steps depend on the original Kripke structure. Let M be the given structure. We analyze each step separately (a naive analysis) 1. First, the algorithm constructs equivalence classes. To do that it needs to compute the maximal simulation relation. [PB96,HHK95] showed that this can be done in time O(jSj Delta jRj) Once the algorithm has the simulation relation, the equivalence classes can be constructed in time O(jSj 2 ) Next, the algorithm constructs the transition relation. This can be done in time O(jSj jRj) As a whole, building the quotient ....

R. Paige and B. Bloom. Transformational design and implementation of new efficient solution to the ready simulation problem. In Science of Computer Programming, volume 24, pages 189--220, 1996. 23

....higher level a language is, the easier it is to do equality reasoning and other analyses for it. For example, using techniques similar to incrementalization on a set theoretic language [61, 58] Paige and others have derived a number of new and improved algorithms for various applications, e.g. [62, 11, 33]. It is well known that features like goto, pointers, and higher order functions are generally difficult to analyze, but seldom are straightforward programs or algorithms first written using them. Precise characterization of these needs to be studied specially. Finally, it is not yet known how to ....

B. Bloom and R. Paige. Transformational design and implementation of a new efficient solution to the ready simulation problem. Sci. Comput. Program., 24(3):189--220, 1995.

.... to the refinement of reactive systems [1, 29, 30] Polynomial time algorithms for computing similarity quotients are presented in [6] O(mn 6 ) 14] O(mn 4 ) and [15] O(m 2 ) Recently it has come to our attention that an O(mn) algorithm was found independently by Bloom and Paige [8]. All of these algorithms are set in somewhat different contexts, and solve somewhat different problems, but can be translated into our framework. A symbolic procedure for model checking 8CTL formulas is given in [17] While that procedure can be used for computing similarity quotients ....

.... automaton and a finite automaton, which is known to be decidable [16] Theorem 3.2 The LTL model checking problem is decidable for generalized 2D rectangular automata. Acknowledgment. The authors thank Rance Cleaveland for providing many valuable pointers to the literature, in particular to [8] and to [12] which presents an O(n 3 ) algorithm for computing more general preorders than simulations on finite graphs. ....

B. Bloom, R. Paige. Transformational design and implementation of a new efficient solution to the ready simulation problem. Science of Computer Programming, to appear.

.... that, when given a list as input (which we will assume has duplicate elements) produces the list representing its powerset . For example, we should compute ( 1] 1] 1; 2] 1] 2] 1; 2] 1; 2; 3] 1] 2] 1; 2] [3]; 1; 3] 2; 3] 1; 2; 3] We use the formalism of lists here to properly demarcate the sequences of sequences. We can find powerlists with the following feedback definition: f(r; s) map (x: x [last(r) s n ) where n = 2 jjrjj Gamma1 (r) X jjrjj X i=0 f(r i ; ....

.... [ 1] 1] 1; 2] f( 1] 1] f( 1; 2] 1; 2] 1] 2] 1; 2] 1] 2] 1; 2] 1; 2; 3] 1] 2] 1; 2] f( 1; 2; 3] 1; 2; 3] 1] 2] 1; 2] map (x: x [3]) 1] 2] 1; 2] 1] 2] 1; 2] 3] 1; 3] 2; 3] 1; 2; 3] 5.4 Fractal Objects Many fractal objects [14] can be generated with feedback computations. As an instance, the generating sequence of the Cantor set can be characterized with the following equations, where ....

[Article contains additional citation context not shown here]

Bard Bloom and Robert Paige, "Transformational Design and Implementation of a New Efficient Solution To the Ready Simulation Problem", submitted to Science of Computer Programming, September 1993.

....for S holds also for I [BBLS92, GL94] Second, unlike trace containment, the definition of simulation is local, as the relation between two states is based only on their successor states. As a result, it can be checked in polynomial time (quadratic in both S and I) whether S simulates I [CPS93, BP96] and a witnessing relation for simulation can be computed using a symbolic fixpoint procedure [HHK95] The locality advantage is so compelling as to make simulation useful also to researchers that favor trace based specification: in automatic verification, simulation is widely used as an ....

B. Bloom, R. Paige. Transformational design and implementation of a new efficient solution to the ready simulation problem. Science of Computer Programming, 24:189--220, 1996.

....for S holds also for I [BBLS92, GL94] Second, unlike trace containment, the definition of simulation is local, as the relation between two states is based only on their successor states. As a result, it can be checked in polynomial time (quadratic in both S and I) whether S simulates I [CPS93, BP96] and a witnessing relation for simulation can be computed using a symbolic fixpoint procedure [HHK95] The locality advantage is so compelling as to make simulation useful also to researchers that favor trace based specification: in automatic verification, simulation is widely used as an ....

.... 2 2 W 2 such that R 2 (w 2 ; w 0 2 ) and S(w 0 1 ; w 0 2 ) The structure K 2 simulates the structure K 1 if there is a simulation S of K 1 by K 2 such that S( w 1 ; w 2 ) The problem of checking if K 2 simulates K 1 can be solved in time O( jW 1 j jW 2 j) Delta (jR 1 j jR 2 j) BP96, HHK95] If K 2 simulates K 1 , then K 2 trace contains K 1 . If K 1 and K 2 are both deterministic, then similarity coincides with trace containment. The following three alternative definitions of similarity are equivalent to the definition above. The game theoretic view. Consider a two player ....

[Article contains additional citation context not shown here]

B. Bloom, R. Paige. Transformational design and implementation of a new efficient solution to the ready simulation problem. Science of Computer Programming, 24:189--220, 1996.

....for S holds also for I [BBLS92, GL94] Second, unlike trace containment, the definition of simulation is local, as the relation between two states is based only on their successor states. As a result, it can be checked in polynomial time (quadratic in both S and I) whether S simulates I [CPS93, BP96] and a witnessing relation for simulation can be computed using a symbolic fixpoint procedure [HHK95] The locality advantage is so compelling as to make simulation useful also to researchers that favor trace based specification: in automatic verification, simulation is widely used as an ....

.... 0 1 2 W 1 such that R 1 (w 1 ; w 0 1 ) and S(w 0 1 ; w 0 2 ) The structure K 1 simulates the structure K 2 if there is a simulation S of K 2 by K 1 such that S( w 1 ; w 2 ) The problem of checking if K 1 simulates K 2 can be solved in time O( jW 1 j jW 2 j) Delta (jR 1 j jR 2 j) BP96, HHK95] If K 1 simulates K 2 , then K 1 trace contains K 2 . If K 1 and K 2 are both deterministic, then similarity coincides with trace containment. The following three alternative definitions of similarity are equivalent to the definition above. The game theoretic view. Consider a two player ....

[Article contains additional citation context not shown here]

B. Bloom and R. Paige. Transformational design and implementation of a new efficient solution to the ready simulation problem. Science of Computer Programming, 24:189-- 220, 1996.

.... to the refinement of reactive systems [1, 29, 30] Polynomialtime algorithms for computing similarity quotients are presented in [6] O(mn 6 ) 14] O(mn 4 ) and [15] O(m 2 ) Recently it has come to our attention that an O(mn) algorithm was found independently by Bloom and Paige [8]. All of these algorithms are set in somewhat different contexts, and solve somewhat different problems, but can be translated into our framework. A symbolic procedure for modelchecking 8CTL formulas is given in [17] While that procedure can be used for computing similarity quotients ....

.... automaton and a finite automaton, which is known to be decidable [16] Theorem 4 The LTL model checking problem is decidable for generalized 2D rectangular automata. Acknowledgment. The authors thank Rance Cleaveland for providing many valuable pointers to the literature, in particular to [8] and to [12] which presents an O(n 3 ) algorithm for computing more general preorders than simulations on finite graphs. ....

B. Bloom, R. Paige. Transformational design and implementation of a new efficient solution to the ready simulation problem. Science of Computer Programming, to appear.

....derivation. Yet the error was introduced in the same portion of code obtained from application of a variant of the critical transformation that we proved for the DFA minimization derivation. 2. Mathematical Preliminaries Our derivations will fit in the framework of Bloom and Paige (see [7]) where a paper and pencil transformational proof was given for a new improved ready simulation algorithm. That derivation made essential use of a SETL like programming language, three basic transformations to map a fixed point specification into RAM code, and Hoare logic combined with set theory ....

....s i Gamma f i (1) for i = 0; 1; We seek a dominated sequence that takes more steps to reach the fixed point but at less overall cost than the Tarski sequence. Dominated convergence can be used to compute fixed points over a variety of lattice theoretically defined datatypes. In [7] the ready simulation problem was solved by using dominated convergence to compute the fixed point of a set valued function defined on a powerset lattice. If S is a finite nonempty set, then P is a partition of S if and only if P is a set of nonempty mutually disjoint subsets of S whose union is ....

[Article contains additional citation context not shown here]

Bloom, B., and Paige, R., Transformational design and implementation of a new efficient solution to the ready simulation problem, Sci. Comput. Programming 24, No. 3, 1995, pp. 189--220.

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B. Bloom and R. Paige. Transformational Design and Implementation of a New E#cient Solution to the Ready Simulation Problem, Science of Computer Programming 24(1995), pp. 189--220.

No context found.

B. Bloom and R. Paige. Transformational design and implementation of new efficient solution to the ready simulation problem. In Science of Computer Programming, volume 24, pages 189--220, 1996.

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Bard Bloom and Robert Paige. Transformational design and implementation of a new e#cient solution to the ready simulation problem. Science of Computer Programming, 24(3):189--220, 1995.

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