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ORCIDRichard J. Lipton
Richard Jay Lipton
Person information
- affiliation: Georgia Institute of Technology
- affiliation: Princeton University, USA
- award (2014): Knuth Prize
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2010 – 2019
- 2016
[c126]Richard J. Lipton, Rafail Ostrovsky, Vassilis Zikas:
Provably Secure Virus Detection: Using The Observer Effect Against Malware. ICALP 2016: 32:1-32:14- [c125]Alexandra Boldyreva, Taesoo Kim, Richard J. Lipton, Bogdan Warinschi:
Provably-Secure Remote Memory Attestation for Heap Overflow Protection. SCN 2016: 83-103 - 2015
- [i9]Richard J. Lipton, Rafail Ostrovsky, Vassilis Zikas:
Provable Virus Detection: Using the Uncertainty Principle to Protect Against Malware. IACR Cryptol. ePrint Arch. 2015: 728 (2015) - [i8]Alexandra Boldyreva, Taesoo Kim, Richard J. Lipton, Bogdan Warinschi:
Towards Provably-Secure Remote Memory Attestation. IACR Cryptol. ePrint Arch. 2015: 729 (2015) - 2013
- [b1]Richard J. Lipton, Kenneth W. Regan:
People, Problems, and Proofs - Essays from Gödel's Lost Letter: 2010. Springer 2013, ISBN 978-3-642-41421-3, pp. I-XVIII, 1-333 - [j76]Richard J. Lipton, Ryan Williams
:
Amplifying circuit lower bounds against polynomial time, with applications. Comput. Complex. 22(2): 311-343 (2013) - [j75]Parinya Chalermsook, Shiva Kintali, Richard J. Lipton, Danupon Nanongkai:
Graph Pricing Problem on Bounded Treewidth, Bounded Genus and k-Partite Graphs. Chic. J. Theor. Comput. Sci. 2013 (2013) - [j74]Atish Das Sarma, Amita Gajewar, Richard J. Lipton, Danupon Nanongkai:
An Approximate Restatement of the Four-Color Theorem. J. Graph Algorithms Appl. 17(5): 567-573 (2013) - 2012
- [j73]Richard J. Lipton:
Might Turing Have Won a Turing Award? Computer 45(6): 96-97 (2012) - [j72]Subrahmanyam Kalyanasundaram, Richard J. Lipton, Kenneth W. Regan, Farbod Shokrieh:
Improved simulation of nondeterministic Turing machines. Theor. Comput. Sci. 417: 66-73 (2012) - [c124]Richard J. Lipton, Ryan Williams:
Amplifying Circuit Lower Bounds against Polynomial Time with Applications. Computational Complexity Conference 2012: 1-9 - [i7]Richard J. Lipton, Kenneth W. Regan, Atri Rudra:
Simulating Special but Natural Quantum Circuits. CoRR abs/1201.3306 (2012) - [i6]Parinya Chalermsook, Shiva Kintali, Richard J. Lipton, Danupon Nanongkai:
Graph Pricing Problem on Bounded Treewidth, Bounded Genus and k-partite graphs. CoRR abs/1203.1940 (2012) - 2011
- [j71]Atish Das Sarma, Richard J. Lipton, Danupon Nanongkai:
Best-order streaming model. Theor. Comput. Sci. 412(23): 2544-2555 (2011) - [c123]Atish Das Sarma, Ashwin Lall, Danupon Nanongkai, Richard J. Lipton, Jun (Jim) Xu:
Representative skylines using threshold-based preference distributions. ICDE 2011: 387-398 - [c122]Richard J. Lipton, Kenneth W. Regan, Atri Rudra:
Symmetric Functions Capture General Functions. MFCS 2011: 436-447 - [c121]Richard J. Lipton:
Quantum Complexity: Some Recent Results, Some Open Problems, Some Thoughts. TAMC 2011: 171 - 2010
- [j70]Danupon Nanongkai, Atish Das Sarma, Ashwin Lall, Richard J. Lipton, Jun (Jim) Xu:
Regret-Minimizing Representative Databases. Proc. VLDB Endow. 3(1): 1114-1124 (2010) - [c120]Sang Kil Cha, Brian Pak, David Brumley, Richard Jay Lipton:
Platform-independent programs. ACM Conference on Computer and Communications Security 2010: 547-558 - [c119]Jin-yi Cai, Xi Chen, Richard J. Lipton, Pinyan Lu:
On Tractable Exponential Sums. FAW 2010: 148-159 - [c118]Subrahmanyam Kalyanasundaram, Richard J. Lipton, Kenneth W. Regan, Farbod Shokrieh:
Improved Simulation of Nondeterministic Turing Machines. MFCS 2010: 453-464 - [i5]Jin-yi Cai, Xi Chen, Richard J. Lipton, Pinyan Lu:
On Tractable Exponential Sums. CoRR abs/1005.2632 (2010)
2000 – 2009
- 2009
- [j69]Mihail N. Kolountzakis, Richard J. Lipton, Evangelos Markakis, Aranyak Mehta, Nisheeth K. Vishnoi:
On the Fourier spectrum of symmetric Boolean functions. Comb. 29(3): 363-387 (2009) - [j68]Markus Bläser, Moritz Hardt, Richard J. Lipton, Nisheeth K. Vishnoi:
Deterministically testing sparse polynomial identities of unbounded degree. Inf. Process. Lett. 109(3): 187-192 (2009) - [c117]Mostafa H. Ammar, Deeparnab Chakrabarty, Atish Das Sarma, Subrahmanyam Kalyanasundaram, Richard J. Lipton:
Algorithms for Message Ferrying on Mobile ad hoc Networks. FSTTCS 2009: 13-24 - [c116]Atish Das Sarma, Richard J. Lipton, Danupon Nanongkai:
Best-Order Streaming Model. TAMC 2009: 178-191 - [c115]Giovanni Di Crescenzo, Richard J. Lipton:
Social Network Privacy via Evolving Access Control. WASA 2009: 551-560 - 2008
- [j67]Parikshit Gopalan, Venkatesan Guruswami, Richard J. Lipton:
Algorithms for Modular Counting of Roots of Multivariate Polynomials. Algorithmica 50(4): 479-496 (2008) - [j66]Subhash Khot, Richard J. Lipton, Evangelos Markakis, Aranyak Mehta:
Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions. Algorithmica 52(1): 3-18 (2008) - [j65]Saugata Basu, Nayantara Bhatnagar, Parikshit Gopalan, Richard J. Lipton:
Polynomials that Sign Represent Parity and Descartes' Rule of Signs. Comput. Complex. 17(3): 377-406 (2008) - 2007
- [c114]David Cash, Yan Zong Ding, Yevgeniy Dodis, Wenke Lee, Richard J. Lipton, Shabsi Walfish:
Intrusion-Resilient Key Exchange in the Bounded Retrieval Model. TCC 2007: 479-498 - 2006
- [j64]Nayantara Bhatnagar, Parikshit Gopalan, Richard J. Lipton:
Symmetric polynomials over Zm and simultaneous communication protocols. J. Comput. Syst. Sci. 72(2): 252-285 (2006) - [c113]Calton Pu, Steve Webb, Oleg M. Kolesnikov, Wenke Lee, Richard J. Lipton:
Towards the integration of diverse spam filtering techniques. GrC 2006: 17-20 - [c112]Parikshit Gopalan, Venkatesan Guruswami, Richard J. Lipton:
Algorithms for Modular Counting of Roots of Multivariate Polynomials. LATIN 2006: 544-555 - [c111]Giovanni Di Crescenzo, Richard J. Lipton, Shabsi Walfish:
Perfectly Secure Password Protocols in the Bounded Retrieval Model. TCC 2006: 225-244 - 2005
- [j63]Lance Fortnow, Richard J. Lipton, Dieter van Melkebeek, Anastasios Viglas:
Time-space lower bounds for satisfiability. J. ACM 52(6): 835-865 (2005) - [j62]Ben Gum, Richard J. Lipton, Andrea S. LaPaugh, Faith E. Fich:
Estimating the maximum. J. Algorithms 54(1): 105-114 (2005) - [j61]Jun (Jim) Xu, Richard J. Lipton:
On fundamental tradeoffs between delay bounds and computational complexity in packet scheduling algorithms. IEEE/ACM Trans. Netw. 13(1): 15-28 (2005) - [c110]Richard J. Lipton, Evangelos Markakis, Aranyak Mehta, Nisheeth K. Vishnoi:
On the Fourier Spectrum of Symmetric Boolean Functions with Applications to Learning Symmetric Juntas. Computational Complexity Conference 2005: 112-119 - [c109]David Dagon, Wenke Lee, Richard J. Lipton:
Protecting Secret Data from Insider Attacks. Financial Cryptography 2005: 16-30 - [c108]Subhash Khot, Richard J. Lipton, Evangelos Markakis, Aranyak Mehta:
Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions. WINE 2005: 92-101 - 2004
- [c107]Saugata Basu, Nayantara Bhatnagar, Parikshit Gopalan, Richard J. Lipton:
Polynomials That Sign Represent Parity and Descartes Rule of Signs. Computational Complexity Conference 2004: 223-235 - [c106]Nikhil R. Devanur, Richard J. Lipton, Nisheeth K. Vishnoi:
On the Complexity of Hilbert's 17th Problem. FSTTCS 2004: 237-249 - [c105]Richard J. Lipton, Evangelos Markakis:
Nash Equilibria via Polynomial Equations. LATIN 2004: 413-422 - [c104]Richard J. Lipton, Evangelos Markakis, Elchanan Mossel, Amin Saberi:
On approximately fair allocations of indivisible goods. EC 2004: 125-131 - [i4]Nayantara Bhatnagar, Parikshit Gopalan, Richard J. Lipton:
The Degree of Threshold Mod 6 and Diophantine Equations. Electron. Colloquium Comput. Complex.(022) (2004) - 2003
- [j60]Richard J. Lipton, Mitsunori Ogihara, Yechezkel Zalcstein:
A Note on Square Rooting of Time Functions of Turing Machines. Theory Comput. Syst. 36(3): 295-299 (2003) - [j59]George Karakostas, Richard J. Lipton, Anastasios Viglas:
On the complexity of intersecting finite state automata and N L versus N P. Theor. Comput. Sci. 302(1-3): 257-274 (2003) - [c103]Richard J. Lipton, Anastasios Viglas:
Non-uniform Depth of Polynomial Time and Space Simulations. FCT 2003: 311-320 - [c102]Nayantara Bhatnagar, Parikshit Gopalan, Richard J. Lipton:
Symmetric Polynomials over Zm and Simultaneous Communication Protocol. FOCS 2003: 450-459 - [c101]Parikshit Gopalan, Richard J. Lipton, Aranyak Mehta:
Randomized Time-Space Tradeoffs for Directed Graph Connectivity. FSTTCS 2003: 208-216 - [c100]Jun Xu, Richard J. Lipton, Irfan A. Essa, Minho Sung, Yong Zhu:
Mandatory human participation: a new authentication scheme for building secure systems. ICCCN 2003: 547-552 - [c99]Nikhil R. Devanur, Richard J. Lipton, Nisheeth K. Vishnoi:
Who's The Weakest Link? SAGA 2003: 108-116 - [c98]Richard J. Lipton, Evangelos Markakis, Aranyak Mehta:
Playing large games using simple strategies. EC 2003: 36-41 - [c97]Richard J. Lipton, Nisheeth K. Vishnoi:
Deterministic identity testing for multivariate polynomials. SODA 2003: 756-760 - [i3]Nayantara Bhatnagar, Parikshit Gopalan, Richard J. Lipton:
Symmetric Polynomials over Zm and Simultaneous Communication Protocols. Electron. Colloquium Comput. Complex.(047) (2003) - 2002
- [c96]Richard J. Lipton, S. Rajagopalan, Dimitrios N. Serpanos:
Spy: A Method to Secure Clients for Network Services. ICDCS Workshops 2002: 23-28 - [c95]Alessandro Orso, Donglin Liang, Mary Jean Harrold, Richard J. Lipton:
Gamma system: continuous evolution of software after deployment. ISSTA 2002: 65-69 - [c94]Jun (Jim) Xu, Richard J. Lipton:
On fundamental tradeoffs between delay bounds and computational complexity in packet scheduling algorithms. SIGCOMM 2002: 279-292 - [i2]Richard J. Lipton, Neal E. Young:
Simple Strategies for Large Zero-Sum Games with Applications to Complexity Theory. CoRR cs.CC/0205035 (2002) - [i1]Richard J. Lipton, Anastasios Viglas:
Non-uniform Depth of Polynomial Time and Space Simulations. Electron. Colloquium Comput. Complex.(057) (2002) - 2001
- [j58]Dan Boneh, Richard A. DeMillo, Richard J. Lipton:
On the Importance of Eliminating Errors in Cryptographic Computations. J. Cryptol. 14(2): 101-119 (2001) - [c93]Dimitrios N. Serpanos, Richard J. Lipton:
Defense Against Man-in-the-Middle Attack in Client-Server Systems. ISCC 2001: 9-14 - [c92]Ben Gum, Richard J. Lipton:
Cheaper by the Dozen: Batched Algorithms. SDM 2001: 1-11 - 2000
- [j57]Dirk Faulhammer, Richard J. Lipton, Laura F. Landweber:
Fidelity of Enzymatic Ligation for DNA Computing. J. Comput. Biol. 7(6): 839-848 (2000) - [j56]Dirk Faulhammer, Anthony R. Cukras, Richard J. Lipton, Laura F. Landweber:
Molecular computation: RNA solutions to chess problems. Proc. Natl. Acad. Sci. USA 97(4): 1385-1389 (2000) - [j55]Jin-yi Cai, Richard J. Lipton, Yechezkel Zalcstein:
The Complexity of the A B C Problem. SIAM J. Comput. 29(6): 1878-1888 (2000) - [c91]George Karakostas, Richard J. Lipton, Anastasios Viglas:
On the Complexity of Intersecting Finite State Automata. Computational Complexity Conference 2000: 229-234
1990 – 1999
- 1999
- [c90]Anna Gál, Shai Halevi, Richard J. Lipton, Erez Petrank:
Computing from Partial Solutions. Computational Complexity Conference 1999: 34-45 - [c89]Dirk Faulhammer, Anthony R. Cukras, Richard J. Lipton, Laura F. Landweber:
When the Knight falls: On constructing an RNA computer. DNA Based Computers 1999: 1-7 - [c88]Richard J. Lipton, Anastasios Viglas:
On the Complexity of SAT. FOCS 1999: 459-464 - 1998
- [j54]Sigal Ar, Richard J. Lipton, Ronitt Rubinfeld, Madhu Sudan:
Reconstructing Algebraic Functions from Mixed Data. SIAM J. Comput. 28(2): 487-510 (1998) - [c87]Richard J. Lipton, Rafail Ostrovsky:
Micropayments via Efficient Coin-Flipping. Financial Cryptography 1998: 1-15 - 1997
- [c86]Laura F. Landweber, Richard J. Lipton, Michael O. Rabin:
DNA2DNA computations: A potential "killer app?". DNA Based Computers 1997: 161-172 - [c85]Dan Boneh, Richard A. DeMillo, Richard J. Lipton:
On the Importance of Checking Cryptographic Protocols for Faults (Extended Abstract). EUROCRYPT 1997: 37-51 - [c84]Richard J. Lipton, Paul J. Martino, Andy Neitzke:
On the Complexity of a Set-Union Problem. FOCS 1997: 110-115 - [c83]Laura F. Landweber, Richard J. Lipton:
DNA²DNA Computations: A Potential "Killer App"? ICALP 1997: 56-64 - [c82]Dan Boneh, Richard J. Lipton:
Effect of Operators on Straight Line Complexity. ISTCS 1997: 1-5 - [c81]Richard J. Lipton:
DNA2DNA Computation: A Potential Killer Application? NIPS 1997 - 1996
- [j53]Dan Boneh, Christopher Dunworth, Richard J. Lipton, Jirí Sgall:
On the Computational Power of DNA. Discret. Appl. Math. 71(1-3): 79-94 (1996) - [j52]Richard J. Lipton:
On Proving that a Graph has no Large Clique: A Connection with Ramsey Theory. Inf. Process. Lett. 58(1): 39-42 (1996) - [j51]Paul Ammann, Richard J. Lipton, Ravi S. Sandhu:
The Expressive Power of Multi-parent Creation in Monotonic Access Control Models. J. Comput. Secur. 4(2/3): 149-166 (1996) - [c80]Dan Boneh, Richard J. Lipton:
Algorithms for Black-Box Fields and their Application to Cryptography (Extended Abstract). CRYPTO 1996: 283-297 - [c79]Dan Boneh, Christopher Dunworth, Richard J. Lipton, Jirí Sgall:
Making DNA computers error resistant. DNA Based Computers 1996: 163-170 - [c78]Richard J. Lipton:
DNA computations can have global memory. DNA Based Computers 1996: 259-265 - [c77]Masato Edahiro, Richard J. Lipton:
Clock Buffer Placement Algorithm for Wire-Delay-Dominated Timing Model. Great Lakes Symposium on VLSI 1996: 143-147 - [c76]Richard J. Lipton:
DNA computations can have global memory. ICCD 1996: 344-347 - [c75]Dan Boneh, Richard J. Lipton:
A Revocable Backup System. USENIX Security Symposium 1996 - 1995
- [j50]Richard J. Lipton, Jeffrey F. Naughton:
Query Size Estimation by Adaptive Sampling. J. Comput. Syst. Sci. 51(1): 18-25 (1995) - [c74]Dan Boneh, Richard J. Lipton:
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract). CRYPTO 1995: 424-437 - [c73]Dan Boneh, Christopher Dunworth, Richard J. Lipton:
Breaking DES using a molecular computer. DNA Based Computers 1995: 37-65 - [c72]Richard J. Lipton:
Speeding up computations via molecular biology. DNA Based Computers 1995: 67-74 - [c71]Jin-yi Cai, Richard J. Lipton, Luc Longpré, Mitsunori Ogihara, Kenneth W. Regan, D. Sivakumar:
Communication Complexity of Key Agreement on Small Ranges. STACS 1995: 38-49 - [e5]Richard J. Lipton, Eric B. Baum:
DNA Based Computers, Proceedings of a DIMACS Workshop, Princeton, New Jersey, USA, April 4, 1995. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 27, DIMACS/AMS 1995, ISBN 978-0-8218-0973-0 [contents] - 1994
- [j49]Jin-yi Cai, Anne Condon, Richard J. Lipton:
PSPACE Is Provable by Two Provers in One Round. J. Comput. Syst. Sci. 48(1): 183-193 (1994) - [j48]Jin-yi Cai, Richard J. Lipton:
Subquadratic Simulations of Balanced Formulae by Branching Programs. SIAM J. Comput. 23(3): 563-572 (1994) - [c70]Richard J. Lipton:
Straight-line complexity and integer factorization. ANTS 1994: 71-79 - [c69]Richard J. Lipton:
Some Consequences of Our Failure to Prove Non-Linear Lower Bounds on Explicit Functions. Computational Complexity Conference 1994: 79-87 - [c68]Jin-yi Cai, Richard J. Lipton, Yechezkel Zalcstein:
The Complexity of the Membership Problem for 2-generated Commutative Semigroups of Rational Matrices. FOCS 1994: 135-142 - [c67]Richard J. Lipton, Andrew Tomkins:
Online Interval Scheduling. SODA 1994: 302-311 - [c66]Richard J. Lipton:
A New Approach To Information Theory. STACS 1994: 699-708 - [c65]Richard J. Lipton, Neal E. Young:
Simple strategies for large zero-sum games with applications to complexity theory. STOC 1994: 734-740 - 1993
- [j47]Richard J. Lipton, Jeffrey F. Naughton:
Clocked Adversaries for Hashing. Algorithmica 9(3): 239-252 (1993) - [j46]Narendra Karmarkar, Richard M. Karp, Richard J. Lipton, László Lovász, Michael Luby:
A Monte-Carlo Algorithm for Estimating the Permanent. SIAM J. Comput. 22(2): 284-293 (1993) - [j45]Richard J. Lipton, Jeffrey F. Naughton, Donovan A. Schneider, S. Seshadri:
Efficient Sampling Strategies for Relational Database Operations. Theor. Comput. Sci. 116(1): 195-226 (1993) - [c64]Jin-yi Cai, Richard J. Lipton, Robert Sedgewick, Andrew Chi-Chih Yao:
Towards Uncheatable benchmarks. Computational Complexity Conference 1993: 2-11 - [c63]Dan Boneh, Richard J. Lipton:
Amplification of Weak Learning under the Uniform Distribution. COLT 1993: 347-351 - [c62]Avrim Blum, Merrick L. Furst, Michael J. Kearns, Richard J. Lipton:
Cryptographic Primitives Based on Hard Learning Problems. CRYPTO 1993: 278-291 - 1992
- [j44]Andrea S. LaPaugh, Richard J. Lipton, Jonathan S. Sandberg:
How to Store a Triangular Matrix. IEEE Trans. Computers 41(7): 896-899 (1992) - [j43]Jin-yi Cai, Anne Condon, Richard J. Lipton:
On Games of Incomplete Information. Theor. Comput. Sci. 103(1): 25-38 (1992) - [c61]Paul Ammann, Richard J. Lipton, Ravi S. Sandhu:
The Expressive Power of Multi-Parent Creation in a Monotonic Access Control Model. CSFW 1992: 148-156 - [c60]Sigal Ar, Richard J. Lipton, Ronitt Rubinfeld, Madhu Sudan:
Reconstructing Algebraic Functions from Mixed Data. FOCS 1992: 503-512 - [c59]Kenneth Salem, Daniel Barbará, Richard J. Lipton:
Probabilistic Dignosis of Hot Spots. ICDE 1992: 30-39 - 1991
- [j42]Noga Alon, Daniel J. Kleitman, Richard J. Lipton, Roy Meshulam, Michael O. Rabin, Joel H. Spencer:
Set systems with no union of cardinality 0 modulom. Graphs Comb. 7(2): 97-99 (1991) - [j41]Daniel Barbará, Richard J. Lipton:
A Class of Randomized Strategies for Low-Cost Comparison of File Copies. IEEE Trans. Parallel Distributed Syst. 2(2): 160-170 (1991) - [j40]Richard A. DeMillo, Richard J. Lipton:
Defining Software by Continuous, Smooth Functions. IEEE Trans. Software Eng. 17(4): 383-384 (1991) - [c58]Jin-yi Cai, Anne Condon, Richard J. Lipton:
PSPACE Is Provable By Two Provers In One Round. Computational Complexity Conference 1991: 110-115 - [c57]Peter Gemmell, Richard J. Lipton, Ronitt Rubinfeld, Madhu Sudan, Avi Wigderson:
Self-Testing/Correcting for Polynomials and for Approximate Functions. STOC 1991: 32-42 - 1990
- [j39]Richard J. Lipton, Arvin Park:
The Processor Identity Problem. Inf. Process. Lett. 36(2): 91-94 (1990) - [c56]Jin-yi Cai, Anne Condon, Richard J. Lipton:
On Bounded Round Multi-Prover Interactive Proof Systems. Computational Complexity Conference 1990: 45-54 - [c55]Richard J. Lipton, Dimitrios N. Serpanos:
Uniform-Cost Communication in Scalable Multiprocessors. ICPP (1) 1990: 429-432 - [c54]Richard J. Lipton, Jeffrey F. Naughton:
Query Size Estimation by Adaptive Sampling. PODS 1990: 40-46 - [c53]Richard J. Lipton, Jeffrey F. Naughton, Donovan A. Schneider:
Practical Selectivity Estimation through Adaptive Sampling. SIGMOD Conference 1990: 1-11 - [c52]Jin-yi Cai, Anne Condon, Richard J. Lipton:
Playing Games of Incomplete Information. STACS 1990: 58-69 - [c51]Richard J. Lipton:
Efficient Checking of Computations. STACS 1990: 207-215
1980 – 1989
- 1989
- [j38]Arvin Park, Krishnaswamy Balasubramanian, Richard J. Lipton:
Array Access Bounds for Block Storage Memory Systems. IEEE Trans. Computers 38(6): 909-913 (1989) - [c50]Richard J. Lipton:
New Directions In Testing. Distributed Computing And Cryptography 1989: 191-202 - [c49]Anne Condon, Richard J. Lipton:
On the Complexity of Space Bounded Interactive Proofs (Extended Abstract). FOCS 1989: 462-467 - [c48]Jin-yi Cai, Richard J. Lipton:
Subquadratic Simulations of Circuits by Branching Programs. FOCS 1989: 568-573 - [c47]Daniel Barbará, Richard J. Lipton:
A Randomized Technique for Remote File Comparison. ICDCS 1989: 12-21 - [c46]