Pub Date : 2014-10-21DOI: 10.1109/FMCAD.2014.6987596
Xin Chen, S. Sankaranarayanan, E. Ábrahám
We propose an approach for computing under- as well as over-approximations for the reachable sets of continuous systems which are defined by non-linear Ordinary Differential Equations (ODEs). Given a compact and connected initial set of states, described by a system of polynomial inequalities, we compute under-approximations of the set of states reachable over time. Our approach is based on a simple yet elegant technique to obtain an accurate Taylor model over-approximation for a backward flowmap based on well-known techniques to over-approximate the forward map. Next, we show that this over-approximation can be used to yield both over- and under-approximations for the forward reachable sets. Based on the result, we are able to conclude "may" as well as "must" reachability to prove properties or conclude the existence of counterexamples. A prototype of the approach is implemented and its performance is evaluated over a reasonable number of benchmarks.
{"title":"Under-approximate flowpipes for non-linear continuous systems","authors":"Xin Chen, S. Sankaranarayanan, E. Ábrahám","doi":"10.1109/FMCAD.2014.6987596","DOIUrl":"https://doi.org/10.1109/FMCAD.2014.6987596","url":null,"abstract":"We propose an approach for computing under- as well as over-approximations for the reachable sets of continuous systems which are defined by non-linear Ordinary Differential Equations (ODEs). Given a compact and connected initial set of states, described by a system of polynomial inequalities, we compute under-approximations of the set of states reachable over time. Our approach is based on a simple yet elegant technique to obtain an accurate Taylor model over-approximation for a backward flowmap based on well-known techniques to over-approximate the forward map. Next, we show that this over-approximation can be used to yield both over- and under-approximations for the forward reachable sets. Based on the result, we are able to conclude \"may\" as well as \"must\" reachability to prove properties or conclude the existence of counterexamples. A prototype of the approach is implemented and its performance is evaluated over a reasonable number of benchmarks.","PeriodicalId":363683,"journal":{"name":"2014 Formal Methods in Computer-Aided Design (FMCAD)","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128613362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-10-21DOI: 10.1109/FMCAD.2014.6987615
E. Tronci, Toni Mancini, Ivano Salvo, S. Sinisi, F. Mari, I. Melatti, A. Massini, Francesco Davi, T. Dierkes, R. Ehrig, S. Röblitz, B. Leeners, T. Kruger, M. Egli, F. Ille
One of the main goals of systems biology models in a health-care context is to individualise models in order to compute patient-specific predictions for the time evolution of species (e.g., hormones) concentrations. In this paper we present a statistical model checking based approach that, given an inter-patient model and a few clinical measurements, computes a value for the model parameter vector (model individualisation) that, with high confidence, is a global minimum for the function evaluating the mismatch between the model predictions and the available measurements. We evaluate effectiveness of the proposed approach by presenting experimental results on using the GynCycle model (describing the feedback mechanisms regulating a number of reproductive hormones) to compute patient-specific predictions for the time evolution of blood concentrations of E2 (Estradiol), P4 (Progesterone), FSH (Follicle-Stimulating Hormone) and LH (Luteinizing Hormone) after a certain number of clinical measurements.
{"title":"Patient-specific models from inter-patient biological models and clinical records","authors":"E. Tronci, Toni Mancini, Ivano Salvo, S. Sinisi, F. Mari, I. Melatti, A. Massini, Francesco Davi, T. Dierkes, R. Ehrig, S. Röblitz, B. Leeners, T. Kruger, M. Egli, F. Ille","doi":"10.1109/FMCAD.2014.6987615","DOIUrl":"https://doi.org/10.1109/FMCAD.2014.6987615","url":null,"abstract":"One of the main goals of systems biology models in a health-care context is to individualise models in order to compute patient-specific predictions for the time evolution of species (e.g., hormones) concentrations. In this paper we present a statistical model checking based approach that, given an inter-patient model and a few clinical measurements, computes a value for the model parameter vector (model individualisation) that, with high confidence, is a global minimum for the function evaluating the mismatch between the model predictions and the available measurements. We evaluate effectiveness of the proposed approach by presenting experimental results on using the GynCycle model (describing the feedback mechanisms regulating a number of reproductive hormones) to compute patient-specific predictions for the time evolution of blood concentrations of E2 (Estradiol), P4 (Progesterone), FSH (Follicle-Stimulating Hormone) and LH (Luteinizing Hormone) after a certain number of clinical measurements.","PeriodicalId":363683,"journal":{"name":"2014 Formal Methods in Computer-Aided Design (FMCAD)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125361753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-10-21DOI: 10.1109/FMCAD.2014.6987604
Pavel Jancík, J. Kofroň, Simone Rollini, N. Sharygina
Craig interpolants are widely used in program verification as a means of abstraction. In this paper, we (i) introduce Partial Variable Assignment Interpolants (PVAIs) as a generalization of Craig interpolants. A variable assignment focuses computed interpolants by restricting the set of clauses taken into account during interpolation. PVAIs can be for example employed in the context of DAG interpolation, in order to prevent unwanted out-of-scope variables to appear in interpolants. Furthermore, we (ii) present a way to compute PVAIs for propositional logic based on an extension of the Labeled Interpolation Systems, and (iii) analyze the strength of computed interpolants and prove the conditions under which they have the path interpolation property.
{"title":"On interpolants and variable assignments","authors":"Pavel Jancík, J. Kofroň, Simone Rollini, N. Sharygina","doi":"10.1109/FMCAD.2014.6987604","DOIUrl":"https://doi.org/10.1109/FMCAD.2014.6987604","url":null,"abstract":"Craig interpolants are widely used in program verification as a means of abstraction. In this paper, we (i) introduce Partial Variable Assignment Interpolants (PVAIs) as a generalization of Craig interpolants. A variable assignment focuses computed interpolants by restricting the set of clauses taken into account during interpolation. PVAIs can be for example employed in the context of DAG interpolation, in order to prevent unwanted out-of-scope variables to appear in interpolants. Furthermore, we (ii) present a way to compute PVAIs for propositional logic based on an extension of the Labeled Interpolation Systems, and (iii) analyze the strength of computed interpolants and prove the conditions under which they have the path interpolation property.","PeriodicalId":363683,"journal":{"name":"2014 Formal Methods in Computer-Aided Design (FMCAD)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124261709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-10-21DOI: 10.1109/FMCAD.2014.6987614
Karsten Scheibler, B. Becker
This work is motivated by (1) a practical application which automatically generates test patterns for integrated circuits and (2) the observation that off-the-shelf state-of-the-art pseudo-Boolean solvers have difficulties in solving instances with huge pseudo-Boolean constraints as created by our application. Derived from the SMT solver iSAT3 we present the solver iSAT3p that on the one hand allows the efficient handling of huge pseudo-Boolean constraints with several thousand summands and large integer coefficients. On the other hand, experimental results demonstrate that at the same time iSAT3p is competitive or even superior to other solvers on standard pseudo-Boolean benchmark families.
{"title":"Using interval constraint propagation for pseudo-Boolean constraint solving","authors":"Karsten Scheibler, B. Becker","doi":"10.1109/FMCAD.2014.6987614","DOIUrl":"https://doi.org/10.1109/FMCAD.2014.6987614","url":null,"abstract":"This work is motivated by (1) a practical application which automatically generates test patterns for integrated circuits and (2) the observation that off-the-shelf state-of-the-art pseudo-Boolean solvers have difficulties in solving instances with huge pseudo-Boolean constraints as created by our application. Derived from the SMT solver iSAT3 we present the solver iSAT3p that on the one hand allows the efficient handling of huge pseudo-Boolean constraints with several thousand summands and large integer coefficients. On the other hand, experimental results demonstrate that at the same time iSAT3p is competitive or even superior to other solvers on standard pseudo-Boolean benchmark families.","PeriodicalId":363683,"journal":{"name":"2014 Formal Methods in Computer-Aided Design (FMCAD)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122639007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-10-21DOI: 10.1109/FMCAD.2014.6987608
Peizun Liu, T. Wahl
Assertion checking for non-recursive unbounded-thread Boolean programs can be performed in principle by converting the program into an infinite-state transition system such as a Petri net and subjecting the system to a coverability check, for which sound and complete algorithms exist. Said conversion adds, however, an additional heavy burden to these already expensive algorithms, as the number of system states is exponential in the size of the program. Our solution to this problem avoids the construction of a Petri net and instead applies the coverability algorithm directly to the Boolean program. A challenge is that, in the presence of advanced communication primitives such as broadcasts, the coverability algorithm proceeds backwards, requiring a backward execution of the program. The benefit of avoiding the up-front transition system construction is that "what you see is what you pay": only system states backward-reachable from the target state are generated, often resulting in dramatic savings. We demonstrate this using Boolean programs constructed by the SatAbs predicate abstraction engine.
{"title":"Infinite-state backward exploration of Boolean broadcast programs","authors":"Peizun Liu, T. Wahl","doi":"10.1109/FMCAD.2014.6987608","DOIUrl":"https://doi.org/10.1109/FMCAD.2014.6987608","url":null,"abstract":"Assertion checking for non-recursive unbounded-thread Boolean programs can be performed in principle by converting the program into an infinite-state transition system such as a Petri net and subjecting the system to a coverability check, for which sound and complete algorithms exist. Said conversion adds, however, an additional heavy burden to these already expensive algorithms, as the number of system states is exponential in the size of the program. Our solution to this problem avoids the construction of a Petri net and instead applies the coverability algorithm directly to the Boolean program. A challenge is that, in the presence of advanced communication primitives such as broadcasts, the coverability algorithm proceeds backwards, requiring a backward execution of the program. The benefit of avoiding the up-front transition system construction is that \"what you see is what you pay\": only system states backward-reachable from the target state are generated, often resulting in dramatic savings. We demonstrate this using Boolean programs constructed by the SatAbs predicate abstraction engine.","PeriodicalId":363683,"journal":{"name":"2014 Formal Methods in Computer-Aided Design (FMCAD)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133907409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-10-21DOI: 10.1109/FMCAD.2014.6987591
Benjamin Bittner, M. Bozzano, A. Cimatti, M. Gario, A. Griggio
Designers are often required to explore alternative solutions, trading off along different dimensions (e.g., power consumption, weight, cost, reliability, response time). Such exploration can be encoded as a problem of parameter synthesis, i.e., finding a parameter valuation (representing a design solution) such that the corresponding system satisfies a desired property. In this paper, we tackle the problem of parameter synthesis with multi-dimensional cost functions by finding solutions that are in the Pareto front: in the space of best trade-offs possible. We propose several algorithms, based on IC3, that interleave in various ways the search for parameter valuations that satisfy the property, and the optimization with respect to costs. The most effective one relies on the reuse of inductive invariants and on the extraction of unsatisfiable cores to accelerate convergence. Our experimental evaluation shows the feasibility of the approach on practical benchmarks from diagnosability synthesis and product-line engineering, and demonstrates the importance of a tight integration between model checking and cost optimization.
{"title":"Towards Pareto-optimal parameter synthesis for monotonie cost functions","authors":"Benjamin Bittner, M. Bozzano, A. Cimatti, M. Gario, A. Griggio","doi":"10.1109/FMCAD.2014.6987591","DOIUrl":"https://doi.org/10.1109/FMCAD.2014.6987591","url":null,"abstract":"Designers are often required to explore alternative solutions, trading off along different dimensions (e.g., power consumption, weight, cost, reliability, response time). Such exploration can be encoded as a problem of parameter synthesis, i.e., finding a parameter valuation (representing a design solution) such that the corresponding system satisfies a desired property. In this paper, we tackle the problem of parameter synthesis with multi-dimensional cost functions by finding solutions that are in the Pareto front: in the space of best trade-offs possible. We propose several algorithms, based on IC3, that interleave in various ways the search for parameter valuations that satisfy the property, and the optimization with respect to costs. The most effective one relies on the reuse of inductive invariants and on the extraction of unsatisfiable cores to accelerate convergence. Our experimental evaluation shows the feasibility of the approach on practical benchmarks from diagnosability synthesis and product-line engineering, and demonstrates the importance of a tight integration between model checking and cost optimization.","PeriodicalId":363683,"journal":{"name":"2014 Formal Methods in Computer-Aided Design (FMCAD)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134086342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-10-21DOI: 10.1109/FMCAD.2014.6987611
Aina Niemetz, Mathias Preiner, Armin Biere
Lemmas on demand is an abstraction/refinement technique for procedures deciding Satisfiability Modulo Theories (SMT), which iteratively refines full candidate models of the formula abstraction until convergence. In this paper, we introduce a dual propagation-based technique for optimizing lemmas on demand by extracting partial candidate models via don't care reasoning on full candidate models. Further, we compare our approach to a justification-based approach similar to techniques employed in the context of model checking. We implemented both optimizations in our SMT solver Boolector and provide an extensive experimental evaluation, which shows that by enhancing lemmas on demand with don't care reasoning, the number of lemmas generated, and consequently the solver runtime, is reduced considerably.
{"title":"Turbo-charging Lemmas on demand with don't care reasoning","authors":"Aina Niemetz, Mathias Preiner, Armin Biere","doi":"10.1109/FMCAD.2014.6987611","DOIUrl":"https://doi.org/10.1109/FMCAD.2014.6987611","url":null,"abstract":"Lemmas on demand is an abstraction/refinement technique for procedures deciding Satisfiability Modulo Theories (SMT), which iteratively refines full candidate models of the formula abstraction until convergence. In this paper, we introduce a dual propagation-based technique for optimizing lemmas on demand by extracting partial candidate models via don't care reasoning on full candidate models. Further, we compare our approach to a justification-based approach similar to techniques employed in the context of model checking. We implemented both optimizations in our SMT solver Boolector and provide an extensive experimental evaluation, which shows that by enhancing lemmas on demand with don't care reasoning, the number of lemmas generated, and consequently the solver runtime, is reduced considerably.","PeriodicalId":363683,"journal":{"name":"2014 Formal Methods in Computer-Aided Design (FMCAD)","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132220665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-10-21DOI: 10.1109/FMCAD.2014.6987598
B. Cook, Heidy Khlaaf, Nir Piterman
In this paper, we describe a new symbolic model checking procedure for CTL verification of infinite-state programs. Our procedure exploits the natural decomposition of the state space given by the control-flow graph in combination with the nesting of temporal operators to optimize reasoning performed during symbolic model checking. An experimental evaluation against competing tools demonstrates that our approach not only gains orders-of-magnitude performance improvement, but also allows for scalability of temporal reasoning for larger programs.
{"title":"Faster temporal reasoning for infinite-state programs","authors":"B. Cook, Heidy Khlaaf, Nir Piterman","doi":"10.1109/FMCAD.2014.6987598","DOIUrl":"https://doi.org/10.1109/FMCAD.2014.6987598","url":null,"abstract":"In this paper, we describe a new symbolic model checking procedure for CTL verification of infinite-state programs. Our procedure exploits the natural decomposition of the state space given by the control-flow graph in combination with the nesting of temporal operators to optimize reasoning performed during symbolic model checking. An experimental evaluation against competing tools demonstrates that our approach not only gains orders-of-magnitude performance improvement, but also allows for scalability of temporal reasoning for larger programs.","PeriodicalId":363683,"journal":{"name":"2014 Formal Methods in Computer-Aided Design (FMCAD)","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114708930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-10-21DOI: 10.1109/FMCAD.2014.6987590
B. Bingham, M. Greenstreet
A response property is a simple liveness property that, given state predicates p and q, asserts "whenever a p-state is visited, a g-state will be visited in the future". This paper presents an efficient and scalable implementation for explicit-state model of checking response properties on systems with strongly- and weakly-fair actions, using a network of machines. Our approach is a novel twist on the One-Way-Catch-Them-Young (OWCTY) algorithm. Although OWCTY has a worst-case time complexity of O(n2m) where n is the number of states of the model, and m is the number of fair actions, we show that in practice, the run-time is a very small multiple of n. This allows our approach to handle large models with a large number of fairness constraints. Our implementation builds upon PREACH, a distributed, explicit-state model checking tool. We demonstrate the effectiveness of our approach by applying it to several standard benchmarks on some real-world, proprietary, architectural models.
{"title":"Response property checking via distributed state space exploration","authors":"B. Bingham, M. Greenstreet","doi":"10.1109/FMCAD.2014.6987590","DOIUrl":"https://doi.org/10.1109/FMCAD.2014.6987590","url":null,"abstract":"A response property is a simple liveness property that, given state predicates p and q, asserts \"whenever a p-state is visited, a g-state will be visited in the future\". This paper presents an efficient and scalable implementation for explicit-state model of checking response properties on systems with strongly- and weakly-fair actions, using a network of machines. Our approach is a novel twist on the One-Way-Catch-Them-Young (OWCTY) algorithm. Although OWCTY has a worst-case time complexity of O(n2m) where n is the number of states of the model, and m is the number of fair actions, we show that in practice, the run-time is a very small multiple of n. This allows our approach to handle large models with a large number of fairness constraints. Our implementation builds upon PREACH, a distributed, explicit-state model checking tool. We demonstrate the effectiveness of our approach by applying it to several standard benchmarks on some real-world, proprietary, architectural models.","PeriodicalId":363683,"journal":{"name":"2014 Formal Methods in Computer-Aided Design (FMCAD)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126220301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-10-21DOI: 10.1109/FMCAD.2014.6987584
Armin Biere
Summary form only given. Bit-precise reasoning (BPR) precisely captures the semantics of systems down to each individual bit and thus is essential to many verification and synthesis tasks for both hardware and software systems. As an instance of Satisfiabiliy Modulo Theories (SMT), BPR is in essence about word-level decision procedures for the theory of bit-vectors. In practice, quantiers and other theory extensions, such as reasoning about arrays, are important too. In the first part of the tutorial we gave a brief overview on basic techniques for bit-precise reasoning and then covered more recent theoretical results, including complexity classification results. We discussed challenges in developping an efficient SMT solver for bit-vectors, like our award winning SMT solver Boolector, and in particular presented examples, for which current techniques fail. Finally, we reviewed the state-of-the-art in word-level model checking, and argued why it is necessary to put more effort in this direction of research.
{"title":"Challenges in bit-precise reasoning","authors":"Armin Biere","doi":"10.1109/FMCAD.2014.6987584","DOIUrl":"https://doi.org/10.1109/FMCAD.2014.6987584","url":null,"abstract":"Summary form only given. Bit-precise reasoning (BPR) precisely captures the semantics of systems down to each individual bit and thus is essential to many verification and synthesis tasks for both hardware and software systems. As an instance of Satisfiabiliy Modulo Theories (SMT), BPR is in essence about word-level decision procedures for the theory of bit-vectors. In practice, quantiers and other theory extensions, such as reasoning about arrays, are important too. In the first part of the tutorial we gave a brief overview on basic techniques for bit-precise reasoning and then covered more recent theoretical results, including complexity classification results. We discussed challenges in developping an efficient SMT solver for bit-vectors, like our award winning SMT solver Boolector, and in particular presented examples, for which current techniques fail. Finally, we reviewed the state-of-the-art in word-level model checking, and argued why it is necessary to put more effort in this direction of research.","PeriodicalId":363683,"journal":{"name":"2014 Formal Methods in Computer-Aided Design (FMCAD)","volume":"228 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132414410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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