Ramakrishna YS, Ramakrishnan CR, Ramakrishnan IV, Smolka SA, Swift T, Warren DS. Efficient model checking using tabled resolution. Proceedings of the 9th International Conference on Computer Aided Verification (CAV), Haifa Israel, July 1997 (Lecture Notes in Computer Science, vol. 1243). Springer: Berlin, 1997; 143--154.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....algorithms [4] may be adapted for computing forced simulation [11] In this report we demonstrate the advantages of using XSB, a tabled logic programming system, to implement a formal IP matching tool. XSB has already been used for building efficient model checkers and bisimulation checkers [12]. We employed some features such as tabling and constraint propagation to build an efficient matching tool. This report is organized as follows: In chapter 2 we develop the formal framework for IP matching using forced simulation. In chapter 3 we show how the matching algorithm can be encoded in ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. W. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In 9th International Conference on Computer Aided Verification, 1997. 16

....no loss of messages. Finally, in Section 4.7 we compare our work with other verification techniques proposed in the literature. Among them we have given special attention to those techniques which use logic programming, constraints, tabled resolution, program analysis, and program transformation [20, 30, 47, 67, 69]. 4.1 A Preliminary Example In this section we illustrate the basic ideas of our verification method by means of a simple example. Let us consider a system Count consisting of an integer counter X which is initialized to 1 and is incremented by 1 at each time unit. The state of the system is the ....

....state systems by incorporating into model checking some abstraction and deduction techniques (see [77] for a brief survey) Recent papers also demonstrate the usefulness of logic programming and constraint logic programming as a basis for the verification of finite or infinite state systems. In [67] the authors present XMC, a model checking system implemented in the tabulation based logic programming language XSB[71] XMC can verify temporal properties expressed in the alternation free fragment of the p calculus of finite state concurrent systems specified in a CCS like language. The XMC ....

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RAMAKRISHNA, Y. S., RAMAKRISHNAN, C. R., RAMAKRISHNAN, I. V., SMOLKA, S. A., SWIFT, T., AND WARREN, D. S. Efficient model check- ing using tabled resolution. In CAV '97 (1997), Lecture Notes in Com- puter Science 1254, Springer-Verlag, pp. 143-154.

....is then exhaustively explored to decide whether a given specification holds for all reachable states. Recently there has been interest in applying logic programming techniques to model checking. Table based logic programming can be used as an efficient means of performing explicit model checking [33]. The possibility of using set based logic program analysis to achieve model checking is explored in [7] Infinite Model Checking However, most software systems cannot be modelled by a finite LTS (or similar system) Indeed, only the most trivial programs can be mapped to a finite state system: ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In O. Grumberg, editor, Proceedings of the International Conference on Computer-Aided Verification (CAV'97), LNCS 1254, pages 143--154. Springer-Verlag, 1997.

....logic program specialisation for infinite state model checking. 1 Introduction Recently there has been interest in applying logic programming techniques to model checking. Table based logic programming and set based analysis can be used as an efficient means of performing explicit model checking [29][4] Despite the success of model checking, most systems must still be substantially simplified and considerable human ingenuity is required to arrive at the stage where the push button automation can be applied [31] Furthermore, most software systems cannot be modelled directly by a finite state ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings CAV'97, LNCS 1254, pages 143--154. Springer-Verlag, 1997.

....Gnu i Protocol Case Study Revisited. Gerard J. Holzmann Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ 07974, USA gerard research.bell labs.com Abstract. In a recent study a series of model checkers, among which Spin [5] SMV [9] and a newer system called XMC [10], were compared on performance. The measurements used for this comparison focused on a model of the i protocol from GNU uucp version 1.04. Eight versions of this iprotocol model were obtained by varying window size, assumptions about the transmission channel, and the presence or absence of a ....

Y.S. Ramakrishna, C.R. Ramakrishnan, et al., Efficient model checking using tabled resolution. Proc. CAV97, LNCS 1254, pp. 143-154, Springer Verlag.

....Other papers in the literature have shown that some real Prolog based applications can obtain much better performance than commercially available C programs. One such case is the XMC system, a model checker written in XSB with tabling that outperforms the well known SPIN model checker written in C [21]. 11 Applications Sicstus Yap XSB XSB T Sicstus C matrix 150 5786032 1710896 1119696 2084168 22497712 matrix 200 9324976 2558696 1830280 3519500 37570992 matrix 300 17189296 4982392 3846680 7531484 78203312 8 queens 2247088 597168 352392 3361200 10 queens 2247088 597224 352392 3361200 ....

Y. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. Smolka, T. Swift, and D. S. Warren. Efficient Model Checking using tabled resolution. In CAV'97, 1997.

....section 4, as well as methods for automata with integer constraints in section 5. Section 6 gives some experimental results obtained with CLP based methods. The paper ends with a discussion in section 7. 2 Encoding Mu Calculus in Tabled Logic Programming This section is essentially borrowed from [40]. The modal mu calculus [32] is an expressive temporal logic whose semantics is usually described over sets of states of labeled transition systems. The logic is encoded is an equational form, the syntax of which is given by the following grammar: F : Z tt ff F F F F ....

....precision, but it is shown in [2] that the computation of least fixed points is actually exact when it terminates. 6 Experimental Results We now review some of the most significant results obtained when running the CLP based systems mentioned above. 6.1 Finite state transition systems XMC. In [40], XMC system is said to have good memory usage on a well known set of benchmarks, as compared to SPIN [29] but its speed appears uneven. The speed weakness of XMC is attributed to the absence of partial order optimization [30] In [15] results from XMC as well as 4 other model checkers are given ....

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Y.S. Ramakrishna, C.R. Ramakrishnan, I.V. Ramakrishnan, S.A. Smolka, T. Swift and D.S. Warren. "Efficient Model Checking Using Tabled Resolution". CAV'97, LNCS 1254, Springer-Verlag, 1997, pp. 143--154.

....domain of regular sets of trees instead of intervals, and Cartesian instead of convex hull approximation. Our characterization of CTL properties can be extended to while programs over numeric data by using constraint logic programs (over numbers instead of trees) as an intermediate layer. In [27], Ramakrishna et al. present an implementation of a model checker for the verification of finite state systems specified by DATALOG programs (i.e. logic programs without function symbols) The correctness of their implementation (in a logic programming language with tabling called XSB) relies ....

....(i.e. logic programs without function symbols) The correctness of their implementation (in a logic programming language with tabling called XSB) relies implicitly on the characterization of CTL properties that we formally prove for logic programs with function symbols. In contrast to the work in [27] which applies programming techniques that that are proper to logic programming languages, we view logic programs rather as an automata theoretic formalism. Structure of the paper. Sections 2 to 4 are to give a flavor of our method, which we present in technical terms in Sections 5 to 7. Section 2 ....

Y. Ramakrishna, C. Ramakrishnan, I. Ramakrishnan, S. Smolka, T. Swift, and D. Warren. Efficient model checking using tabled resolution. In Computer Aided Verification (CAV'97), LNCS 1254. Springer-Verlag, June 1997.

....feature of logic programming systems. Indeed, a number of applications that were either beyond the reach or very difficult to tackle with conventional Prolog systems are now possible using tabled evaluation. Such application areas include, but are not limited to, verification using model checking [10], program analysis [2, 12] and logic based databases [14] Despite this increase in applicability of tabled implementations, for quite a long time, there seemed to be only one possible way of implementing the suspension resumption mechanism that tabling requires in a logic programming system that ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. Swift, and D. S. Warren. Efficient Model Checking Using Tabled Resolution. In O. Grumberg, editor, Proceedings of the 9th International Conference on Computer-Aided Verification, number 1254 in LNCS, pages 143--154, Haifa, Israel, July 1997. Springer-Verlag.

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In O. Grumberg, editor, Proceedings of the 9th International Conference on Computer-Aided Verification, number 1254 in LNCS, pages 143--154, Haifa, Israel, July 1997. Springer.

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Y.S. Ramakrishna, C.R. Ramakrishnan, I.V. Ramakrishnan, Terrance Swift, S.A. Smolka, and D.S. Warren, Efficient model-checking using tabled resolution, Proceedings of CAV'97, June 1997.

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. L. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings of the 9th International Conference on Computer-Aided Verification (CAV '97), Haifa, Israel, July 1997. Springer-Verlag.

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. L. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings of the 9th International Conference on Computer-Aided Verification (CAV '97), Haifa, Israel, July 1997. Springer-Verlag.

....common Prolog engine, the WAM, to produce an engine , the SLG WAM [46,47,26,44] in which tabling can be mixed with Prolog. At a practical level the mixture of tabling and Prolog has been used in numerous applications: in grammar processing [34,15] in program analysis [18,12,9] in model checking [43,14]; in machine learning [33] in diagnosis [22] and as an implementation platform for logical updates [36] While XSB was originally developed at SUNY Stony Brook, current versions are developed in close collaboration between developers at SUNY Stony Brook, Universidade Nova de Lisboa, and ....

....routines is expected to outweigh the reduction in speed. 4.3. The XMC Model Checker The XMC model checker, implemented using XSB, relies on non stratified negation to verify properties of concurrent systems that contain a finite number of states. XMC has been described in the literature [43,14], so that only an overview, focusing on its non monotonic aspects, is provided here. Typically model checkers consist of a process calculus to represent states of processes and their communication methods, along with a temporal logic to reason about sequences of possible system states, given an ....

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings on the Conference on Automated Verification, pages 143--154, 1997.

....features will enable us to directly describe 2 complex processes. In the following, for the purpose of illustration, we choose a value passing language based on Milner s CCS [16] augmented with algebraic datatypes (in the form of Prolog terms) a syntactic variant of the language described in [18]. In CCS, a system is viewed as a collection of processes that can communicate (and synchronize by communicating) along channels. Processes may be combined sequentially (using the ffi operator) or in parallel (using the jj operator) Nondeterministic actions can be captured using the choice ....

Y.S. Ramakrishna, C.R. Ramakrishnan, I.V. Ramakrishnan, Terrance Swift, S.A. Smolka, and D.S. Warren, Efficient model-checking using tabled resolution, Proceedings of CAV'97, June 1997.

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. W. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proc. of CAV'97, 1997.

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. W. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings of the 9th International Conference on Computer-Aided Verification (CAV '97), Haifa, Israel, July 1997. Springer-Verlag.

.... loop Example: Groundness Analysis (from [26] append( Ys,Ys) append( X Xs] Ys, X Zs] append(Xs,Ys,Zs) gappend(g,Y,Y) gappend(X1,Ys,Z1) iff(X1,X,Xs) iff(Z1,X,Zs) gappend(Xs,Ys,Zs) iff(g,g,g) iff(n,n,n) iff(n,n,g) iff(n,g,n) 8 Overview ffl Software Verification [92], 83] ffl The modal mu calculus [76] uses lfp quantification (x) and gfp quantification (x) to test properties of transition systems: Along some computation path, the property P holds infinately often , in the modal mu calculus: x 1 :x 2 : P x 1 ) x 2 ) so a lfp ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings on the Conference on Automated Verification, pages 143--154, 1997.

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings on the Conference on Automated Verification, pages 143--154, 1997.

....the concept of relevance within a tabled evaluation. Keywords: Logic Programming, Non Monotonic Reasoning 1 Introduction The ability to compute queries according to the Well Founded Semantics [19] WFS) and its extensions has proven useful for a number of applications, including model checking [12] and diagnosis [5] Within the logic programming community, evaluation of the WFS is commonly done using tabled evaluation methods [3, 2, 4] Of these, SLG resolution [3] Linear resolution with Selection function for General logic programs) is of interest because it can be used with non ground ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings on the Conference on Automated Verification, pages 143--154, 1997.

No context found.

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. L. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Computer-Aided Verification (CAV '97). Springer Verlag, 1997.

....of declarativeness over traditional (Prolog like) logic programming systems. Availability of tabled logic programming systems makes it feasible to develop a larger class of efficient declarative solutions to complex applications than heretofore possible using traditional Prolog based systems. See [6] for example. At a high level, top down tabling systems evaluate programs by recording subgoals (referred to as calls) and their provable instances (referred to as answers) in a table. Predicates are marked a priori as either tabled or nontabled. Clause resolution, which is the basic mechanism ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. W. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proc. of the 9th Intl. Conf. on Computer-Aided Verification, 1997.

....in [21] and they will be incorporated in the full version of this paper. Interestingly, recent advances in logic programming based model checking [7] open up the possibility of using logic program transformations for the verification of parameterized concurrent systems. The XMC model checker [18], built on top of the XSB tabled logic programming system [25] can verify finite state systems specified using value passing CCS [15] and formulas expressed in modal mu calculus [13] XMC s space and time performance is competitive with hand coded (in C C ) model checkers such as the Concurrency ....

Y.S. Ramakrishna, C.R. Ramakrishnan, I.V. Ramakrishnan, Terrance Swift, S.A. Smolka, and D. S. Warren. Efficient model-checking using tabled resolution. Proceedings of Computer Aided Verification (CAV), 1997.

....applications involving fixed point computations such as program analysis and model checking, which were beyond the reach of traditional LP systems, have now been made feasible with tabled LP. In fact, using the XSB tabled LP system [6] we have constructed program analyzers [8] and model checkers [7, 5] that are competitive (in time and space) with existing systems consisting of much larger programs written in lower level languages. Surprisingly, the power and usefulness of tabled logic programming stems from one simple notion: avoid redundant computation by permitting the use of proven ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. W. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings of the 9th International Conference on Computer-Aided Verification (CAV '97), Haifa, Israel, July 1997. Springer-Verlag.

....answers for a table involves resolution with answers from other already completed tables, the overhead from code generation is usually balanced by the speedup in the time to access these answers. 6.4. Analysis of Space Requirements In this section we analyze space usage on a practical example. In [11] it was shown that model checking of concurrent systems can be implemented using XSB s tabling. Furthermore, it was shown that the resulting system is comparable in both time and space to systems that have been specially designed for model checking. Table 6.6 compares either the number of trie ....

....substitution factoring) 225957 324648 Size of Calls (tries) 4 62216 Size of Returns (tries, no substitution factoring) 63347 62625 Size of Returns (tries, substitution factoring) 63343 58740 TABLE 6.6. Sizes of Hashed Terms and Tries with and without Substitution Factoring 21 As presented in [11], a state of a concurrent system can be represented as a logical term. Such a term may be lengthy, but similar states may share a common prefix when represented as terms. Table 6.6 reflects this sharing through the size reduction of the trie based methods over the hash based methods. In leader, ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. Swift, and D. S. Warren. Efficient Model Checking Using Tabled Resolution. In O. Grumberg, editor, Proceedings of the 9th International Conference on Computer-Aided Verification, number 1254 in LNCS, pages 143--154, Haifa, Israel, July 1997. Springer-Verlag.

No context found.

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. W. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings of the 9th International Conference on Computer-Aided Verification (CAV '97), Haifa, Israel, July 1997. Springer-Verlag.

....for motivating tabling optimizations is shown by formalizing the concept of demand within a tabled evaluation. 1 Introduction The ability to compute queries according to the Well Founded Semantics (WFS) and its extensions has proven useful a number of applications, including model checking [12] and diagnosis [4] Within the logic programming community, evaluation of the WFS is commonly done using tabled evaluation methods [2, 1, 3] Of these, SLG resolution [2] Linear resolution with Selection function for General logic programs) is of interest because it can be used with non ground ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings of CAV 97, 1997.

....First, there are useful programs that are LRD stratified but that do not appear to be contained in lower stratification classes. One example of this is the translation of the alternation free modal calculus [8] 2 , a temporal logic used for model checking, into an LRD stratified program [18]. Second, LRD stratified programs contain other stratification classes as well as common transformations of these programs. The importance of this second point can be seen from the following example. Consider the component testing program from [24] working(X) tested(X) working(X) part(X,Y) ....

Y. Ramakrishna, C. Ramakrishnan, I. Ramakrishnan, S. Smolka, T. Swift, and D. Warren. Efficient model checking using tabled resolution. In Proceedings of CAV 97, 1997.

....termination properties. This property has led to the use of tabled logic programming for new areas of logic programming. These include not only deductive database style applications, but other fixpoint style problems, such as program analysis [8, 6] compiler optimization [7] and model checking [16]. Ensuring that these new applications run efficiently may require the use of different scheduling strategies. The possibility of different useful strategies derives from an intrinsic asynchrony in tabling systems between the generation of answers in one path of a computation and their return to a ....

Y. Ramakrishna, C.R. Ramakrishnan, I.V. Ramakrishnan, S. Smolka, T. Swift, and D. Warren. Efficient model checking using tabled resolution. In Proceedings of Computer Aided Verification (CAV), 1997.

....at the speed of Prolog. This property has led to the use of tabled logic programming for new areas of logic programming. These include not only deductive database style applications, but other fixpoint style problems, such as program analysis [7, 5] compiler optimization [6] and modelchecking [15]. Ensuring that these new applications run efficiently may require the use of different A preliminary version of this paper appeared in Proceedings of the Eigth International Symposium of Programming Languages, Implementations, Logics and Programs, Springer Verlag, 1996, pp. 243 258. ....

Y. Ramakrishna, C.R. Ramakrishnan, I.V. Ramakrishnan, S. Smolka, T. Swift, and D. Warren. Efficient model checking using tabled resolution. In Proceedings of Computer Aided Verification (CAV), 1997.

....extension of SLG that provides a formal framework to model scheduling strategies 1 Introduction Applications of Tabled Logic Programming are becoming common. Many abstract interpreters use tabling (or magic) to determine properties of programs [10, 3, 1] Tabling is also used for model checking [13], for natural language analysis [12, 11] and for medical diagnosis [9] Several reasons account for this profusion of applications, among them the fact that tabled logic programs have a clear declarative semantics in the Well Founded Semantics, several well defined operational semantics, and ....

Y. Ramakrishna, C.R. Ramakrishnan, I.V. Ramakrishnan, S. Smolka, T. Swift, and D. Warren. Efficient model checking using tabled resolution. In Proceedings of Computer Aided Verification (CAV), 1997.

....t 2 1 (e.g. f(a,Y) is an instance of f(X,Y) Tabled resolution methods extend the power of logic programming. New applications, especially those involving deductive databases[1] non monotonic reasoning and problems involving fixpoint computations such as program analysis[6] and model checking[5], that were all beyond the reach of Prolog based systems have now been made feasible. Although the concept of tabled evaluation has been around for more than a decade, practical systems based on tabling are only beginning to appear. Early experience with these systems suggest that they are indeed ....

Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, Scott A. Smolka, Terrance Swift, and David S. Warren. Efficient model checking using tabled resolution (submitted to cav'97). Technical report, SUNY at Stony Brook, 1997.

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Ramakrishna YS, Ramakrishnan CR, Ramakrishnan IV, Smolka SA, Swift T, Warren DS. Efficient model checking using tabled resolution. Proceedings of the 9th International Conference on Computer Aided Verification (CAV), Haifa Israel, July 1997 (Lecture Notes in Computer Science, vol. 1243). Springer: Berlin, 1997; 143--154.

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Y. Ramakrishna, C. Ramakrishnan, I. Ramakrishnan, S. Smolka, T. Swift, and D. Warren. Efficient Model Checking Using Tabled Resolution. Proceedings of the 9th CAV, Haifa Israel, LNCS1243, Springer-Verlag, July 1997.

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Y. Ramakrishna, C. Ramakrishnan, I. Ramakrishnan, S. Smolka, T. Swift, and D. Warren. Efficient Model Checking Using Tabled Resolution. Proceedings of the 9th International Conference on Computer Aided Verification (CAV), Haifa Israel, LNCS1243, Springer Verlag, pages 143--154, July 1997.

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Y.S. Ramakrishna, C.R. Ramakrishnan, I.V. Ramakrishnan, S.A. Smolka, T. Swift, and D.S. Warren. Efficient Model Checking Using Tabled Resolution. Proceedings of the 9th International Conference on Computer Aided Verification (CAV), Haifa Israel, LNCS1243, Springer-Verlag, July 1997.

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Computer-Aided Verification (CAV'97), LNCS 1254, pages 143--154. Springer-Verlag, Berlin, 1997.

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Computer-Aided Verification (CAV'97), LNCS 1254, pages 143--154. Springer-Verlag, Berlin, 1997.

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Orna Grumberg, editor, Proceedings of the 9th International Conference on Computer Aided Verification (CAV '97), LNCS 1254. Springer, Haifa, Israel, July 1997.

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Y. Ramakrishna, C.R. Ramakrishnan, I.V. Ramakrishnan, S. Smolka, T. Swift, and D. Warren. Efficient model checking using tabled resolution. In Proceedings of Computer Aided Verification (CAV), 1997.

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Y. S. Ramakrishna, C. R. Ramakrishnan, I. V. Ramakrishnan, S. A. Smolka, T. W. Swift, and D. S. Warren. Efficient model checking using tabled resolution. In Proceedings of the 9th International Conference on Computer-Aided Verification (CAV '97), Haifa, Israel, July 1997. Springer-Verlag.

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Y. Ramakrishna, C.R. Ramakrishnan, I.V. Ramakrishnan, S. Smolka, T. Swift, and D. Warren. Efficient model checking using tabled resolution. In Proceedings of Computer Aided Verification (CAV), 1997. BIBLIOGRAPHY 100

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