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Xs Are for Trajectory Evaluation, Booleans Are for Theorem Proving [chapter]

Mark D. Aagaard, Thomas F. Melham, John W. O'Leary
1999 Lecture Notes in Computer Science  
We prove a theorem that translates correctness results from trajectory evaluation over a four-valued lattice into a shallow embedding of temporal operators over Boolean streams.  ...  This translation connects the specialized world of trajectory evaluation to a general-purpose logic and provides the semantic basis for connecting additional decision procedures and model checkers.  ...  However, experience with a variety of techniques for combining trajectory evaluation with theorem proving [11, 1] has shown that a purely black box integration is not an effective solution for gate-level  ... 
doi:10.1007/3-540-48153-2_16 fatcat:ayjnr36c3rdr3h2anq7hlkuo4m

An industrially effective environment for formal hardware verification

C.-J.H. Seger, R.B. Jones, J.W. O'Leary, T. Melham, M.D. Aagaard, C. Barrett, D. Syme
2005 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
theorem proving in higher-order logic.  ...  Forte has proven to be effective in large-scale industrial trials and combines an efficient linear-time logic model-checking algorithm, namely the symbolic trajectory evaluation (STE), with lightweight  ...  The authors are particularly grateful to the users of Forte at Intel and to the Intel design teams who supplied case studies for their own example verifications.  ... 
doi:10.1109/tcad.2005.850814 fatcat:rxashd5osrhcjky5mgq2jsodk4

Abstraction by Symbolic Indexing Transformations [chapter]

Thomas F. Melham, Robert B. Jones
2002 Lecture Notes in Computer Science  
Symbolic indexing is a data abstraction technique that exploits the partially-ordered state space of symbolic trajectory evaluation (STE).  ...  We present logical machinery and efficient algorithms that provide a much simpler interface to symbolic indexing for the STE user.  ...  We thank the anonymous referees for their careful reading of the paper and very helpful comments. John Harrison and Ashish Darbari also provided useful remarks on notation.  ... 
doi:10.1007/3-540-36126-x_1 fatcat:4fyl33brirh5dbsbu6yp3e3slu

A two-level formal verification methodology using HOL and COSMOS [chapter]

Carl -Johan H. Seger, Jeffrey J. Joyce
1992 Lecture Notes in Computer Science  
Theorem-proving and symbolic simulation are both described as methods for the formal verification of hardware. They are both used to achieve a common goaJ--correctly designed hardware.  ...  The main significance of this paper--and its most original contribution--is the suggestion that symbolic simulation and theorem-proving can be combined in a complementary manner.  ...  We are currently in the process of formalizing the interface logic and implementing a compiler for this language in the COSMOS system.  ... 
doi:10.1007/3-540-55179-4_29 fatcat:ltyerl2egrhltaiynoi7eof2fq

A novel formalization of symbolic trajectory evaluation semantics in Isabelle/HOL

Yongjian Li, William N.N. Hung, Xiaoyu Song
2011 Theoretical Computer Science  
This paper presents a formal symbolic trajectory evaluation (STE) theory based on a structural netlist circuit model, instead of an abstract next state function.  ...  We introduce an inductive definition for netlists, which gives an accurate and formal definition for netlist structures.  ...  Trajectory evaluation logic. Specifications in STE are symbolic trajectory formulas.  ... 
doi:10.1016/j.tcs.2011.01.032 fatcat:xvydqdwd2zdzddnngtelzpaqu4

Validating PowerPC microprocessor custom memories

N. Krishnamurthy, A.K. Martin, M.S. Abadir, J.A. Abraham
2000 IEEE Design & Test of Computers  
Acknowledgments We thank the entire project and tools teams at Somerset, Motorola, for their cooperation and commitment to the successful conclusion of this project.  ...  in symbolic execution. 4, 9, 13, 14 Symbolic Trajectory Evaluation.  ...  Theorem proving is a technique that works within a framework of logic, with axioms representing known truths about the behavior of hardware and theorems representing newly inferred properties of the system's  ... 
doi:10.1109/54.895007 fatcat:t3w2vughyzem5ot2okcxnb43hm

Automatic Abstraction in Symbolic Trajectory Evaluation

Sara Adams, Magnus Bjork, Tom Melham, Carl-Johan Seger
2007 Formal Methods in Computer Aided Design (FMCAD'07)  
Symbolic trajectory evaluation (STE) is a model checking technology based on symbolic simulation over a lattice of abstract state sets.  ...  The STE algorithm operates over families of these abstractions encoded by Boolean formulas, enabling verification with many different abstraction cases in a single modelchecking run.  ...  INTRODUCTION Symbolic Trajectory Evaluation (STE) is a model checking technology based on symbolic simulation over a lattice of abstract state sets [1] .  ... 
doi:10.1109/famcad.2007.27 dblp:conf/fmcad/AdamsBMS07 fatcat:ijybq3y2ffb5tdrp447755br54

Automatic Abstraction in Symbolic Trajectory Evaluation

Sara Adams, Magnus Bjork, Tom Melham, Carl-Johan Seger
2007 Formal Methods in Computer Aided Design (FMCAD'07)  
Symbolic trajectory evaluation (STE) is a model checking technology based on symbolic simulation over a lattice of abstract state sets.  ...  The STE algorithm operates over families of these abstractions encoded by Boolean formulas, enabling verification with many different abstraction cases in a single modelchecking run.  ...  INTRODUCTION Symbolic Trajectory Evaluation (STE) is a model checking technology based on symbolic simulation over a lattice of abstract state sets [1] .  ... 
doi:10.1109/fmcad.2007.4401991 fatcat:2uyg6sf2pnfifoazquezrjak5m

Implementing Hybrid Semantics: From Functional to Imperative [article]

Sergey Goncharov and Renato Neves and José Proença
2020 arXiv   pre-print
evaluate and inspect hybrid programs, in the spirit of GHCi for Haskell and UTop for OCaml.  ...  We then establish a corresponding soundness and adequacy theorem.  ...  are evaluated).  ... 
arXiv:2009.14322v1 fatcat:zdttbvhbqngr7c6k5jm6jmfo7m

Proof Engineering in the Large: Formal Verification of Pentium®4 Floating-Point Divider [chapter]

Roope Kaivola, Katherine Kohatsu
2001 Lecture Notes in Computer Science  
The verification methodology is based on combining human-guided mechanised theorem-proving with low-level steps verified by fully automated model-checking.  ...  The essential relation between such four-valued and Boolean sequences is that any assertion verified over a sequence containing Xs will hold for sequences with Xs replaced with either T or F [4, 3] .  ...  The interface language to Voss is FL, a strongly-typed functional language in the ML family [16] , model checking is done via symbolic trajectory evaluation (STE) [18] , and theorem proving is done in  ... 
doi:10.1007/3-540-44798-9_18 fatcat:edbycgiag5cvrhacuxm4iyz42e

Formal Verification of Explicitly Parallel Microprocessors [chapter]

Byron Cook, John Launchbury, John Matthews, Dick Kieburtz
1999 Lecture Notes in Computer Science  
Acknowledgments For their contributions to this research, we thank Mark Aagaard Acknowledgements We wish to thank Byron Cook, Sava Krstic, and John Launchbury for their valuable contributions to this  ...  By evaluating test we are proving that, for Boolean vectors of length 8, the counter circuit meets our specification.  ...  For example, symbolic trajectory evaluation (STE) [SB95] is currently being applied at the bit-level using BDDs as a symbolic representation.  ... 
doi:10.1007/3-540-48153-2_4 fatcat:pd5w6ggq6fdpxfeqwiprqxintu

Formal verification of an Intel XScale processor model with scoreboarding, specialized execution pipelines, and impress data-memory exceptions

S.K. Srinivasan, M.N. Velev
2003 First ACM and IEEE International Conference on Formal Methods and Models for Co-Design, 2003. MEMOCODE '03. Proceedings.  
Morrow for answering questions about the Intel Xscale architecture.  ...  Tahar and Kumar [35] proved the correctness of a pipelined DLX with exceptions using the theorem prover HOL [12] .  ...  They used Symbolic Trajectory Evaluation (STE) to verify that the implementation circuit fulfills the ISA that is defined as a set of abstract assertions.  ... 
doi:10.1109/memcod.2003.1210090 dblp:conf/memocode/SrinivasanV03 fatcat:auj4ocrh2rbrfbp7ocvhmtigea

Verifying a Synthesized Implementation of IEEE-754 Floating-Point Exponential Function using HOL

B. Akbarpour, A. T. Abdel-Hamid, S. Tahar, J. Harrison
2009 Computer journal  
Theorem proving, however, offers a better solution to handle such verification.  ...  The high ability of abstraction in the HOL verification system allows its use for the verification task over the whole design path of the circuit, starting from gate level implementation of the circuit  ...  Both the IBM and Intel floating-point verification efforts use symbolic simulation (via ACL2 at IBM and STE (Symbolic Trajectory Evaluation) at Intel) for verification of optimized gate-level designs against  ... 
doi:10.1093/comjnl/bxp023 fatcat:wvf6ehqqefaqtj6yhois52grmy

Proof Artifact Co-training for Theorem Proving with Language Models [article]

Jesse Michael Han, Jason Rute, Yuhuai Wu, Edward W. Ayers, Stanislas Polu
2022 arXiv   pre-print
Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built.  ...  We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32% to 48%.  ...  THEOREM PROVING EVALUATION We run theorem-proving evaluations on our held-out test set, comprising 3071 theorems.  ... 
arXiv:2102.06203v2 fatcat:ly2rlwm2erhjhakw42d2nht2gy

Stability of stationary solutions of piecewise affine differential equations describing gene regulatory networks

Anna Machina, Arcady Ponosov
2011 Journal of Mathematical Analysis and Applications  
The main result of the paper justifies a reduction principle in the stability analysis enabling to omit the variables that are not singular, i.e. that stay away from the discontinuity set of the system  ...  Acknowledgments The authors would like to thank the anonymous referees for a number of corrections and helpful suggestions that affected the article content and presentation of the results.  ...  The theorem is proved. Let us only remark that it is the mean value theorem for multivalued functions that yields the convex hull of F 1 , i.e.  ... 
doi:10.1016/j.jmaa.2011.02.034 fatcat:cpd5uusgerbsjjtye6z6tkit2u
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