Research

Francine Blanchet-Sadri

Areas of Interest



Society Memberships



Book



Book Chapters



Selected Refereed Journals

  1. F. Blanchet-Sadri, "Games, Equations and the Dot-Depth Hierarchy." International Journal of Computers and Mathematics with Applications, Vol. 18, No. 9, 1989, pp 809-822.

  2. F. Blanchet-Sadri, "On Dot-Depth Two." RAIRO-Theoretical Informatics and Applications, Vol. 24, No. 6, 1990, pp 521-529.

  3. F. Blanchet-Sadri, "Games, Equations and Dot-Depth Two Monoids." Discrete Applied Mathematics, Vol. 39, No. 2, 1992, pp 99-111.

  4. F. Blanchet-Sadri, "The Dot-Depth of a Generating Class of Aperiodic Monoids is Computable." International Journal of Foundations of Computer Science, Vol. 3, No. 4, 1992, pp 419-442.

  5. F. Blanchet-Sadri, "Equations and Dot-Depth One." Semigroup Forum, Vo. 47, No. 3, 1993, pp 305-317.

  6. F. Blanchet-Sadri, "Equations and Monoid Varieties of Dot-Depth One and Two." Theoretical Computer Science, Vol. 123, No. 2, 1994, pp 239-258.

  7. F. Blanchet-Sadri and X.-H. Zhang, "Equations on the Semidirect Product of a Finite Semilattice by a Finite Commutative Monoid." Semigroup Forum, Vol. 49, No. 1, 1994, pp 67-81.

  8. F. Blanchet-Sadri, "On a Complete Set of Generators for Dot-Depth Two." Discrete Applied Mathematics, Vol. 50, No. 1, 1994, pp 1-25.

  9. F. Blanchet-Sadri, "Equations on the Semidirect Product of a Finite Semilattice by a J-trivial Monoid of Height k." RAIRO-Theoretical Informatics and Applications, Vol. 29, No. 3, 1995, pp 157-170.

  10. F. Blanchet-Sadri, "Some Logical Characterizations of the Dot-Depth Hierarchy and Applications." Journal of Computer and System Sciences, Vol. 51, No. 2, 1995, pp 324-337.

  11. F. Blanchet-Sadri, "Inclusion Relations between some Congruences related to the Dot-Depth Hierarchy." Discrete Applied Mathematics, Vol. 68, 1996, pp 33-71.

  12. F. Blanchet-Sadri, "On Semidirect and Two-Sided Semidirect Products of Finite J-trivial Monoids." RAIRO-Theoretical Informatics and Applications, Vo. 30, No. 5, 1996, pp 457-482.

  13. F. Blanchet-Sadri, "Equations on Semidirect Product of Commutative Semigroups." Semigroup Forum, Vol. 55, No. 1, 1997, pp 80-88.

  14. F. Blanchet-Sadri, "On the Semidirect Product of the Pseudovariety of Semilattices by a Locally Finite Pseudovariety of Groups." RAIRO-Theoretical Informatics and Applications, Vol. 31, No. 3, 1997, pp 237-250.

  15. F. Blanchet-Sadri and F.D. Gaddis, "On a Product of Finite Monoids." Semigroup Forum, Vol. 57, 1998, pp 75-91.

  16. F. Blanchet-Sadri, "Trees, Congruences and Varieties of Finite Semigroups." Discrete Applied Mathematics, Vol. 86, 1998, pp 157-179.

  17. F. Blanchet-Sadri and C. Morgan, "Multiset and Set Decipherable Codes." International Journal of Computers and Mathematics with Applications, Vol. 41, No. 10/11, 2001, pp 1257-1262.

  18. F. Blanchet-Sadri, "On Unique, Multiset, and Set Decipherability of Three-Word Codes." IEEE Transactions on Information Theory, Vol. 47, No. 5, 2001, pp 1745-1757.

  19. F. Blanchet-Sadri and R.A. Hegstrom, "Partial Words and a Theorem of Fine and Wilf Revisited." Theoretical Computer Science, Vol. 270, No. 1/2, 2002, pp 401-419.

  20. F. Blanchet-Sadri and T. Howell, "Note on Decipherability of Three-Word Codes." International Journal of Mathematics and Mathematical Sciences, Vol. 30, No. 8, 2002, pp 491-504.

  21. F. Blanchet-Sadri and D.K. Luhmann, "Conjugacy on Partial Words." Theoretical Computer Science, Vol. 289, No. 1, 2002, pp 297-312.

  22. F. Blanchet-Sadri, "A Periodicity Result of Partial Words with One Hole." International Journal of Computers and Mathematics with Applications, Vol. 46, No. 5/6, 2003, pp 813-820.

  23. F. Blanchet-Sadri, "Periodicity on Partial Words." International Journal of Computers and Mathematics with Applications, Vol. 47, No. 1, 2004, pp 71-82. 

  24. F. Blanchet-Sadri and A. Chriscoe, "Local Periods and Binary Partial Words: An Algorithm." Theoretical Computer Science, Vol. 314, 2004, pp 189-216.

  25. F. Blanchet-Sadri, "Codes, Orderings, and Partial Words." Theoretical Computer Science, Vol. 329, 2004, pp 177-202.

  26. F. Blanchet-Sadri and S. Duncan, "Partial Words and the Critical Factorization Theorem." Journal of Combinatorial Theory, Series A, Vol. 109, 2005, pp 221-245 (Awarded "Journal of Combinatorial Theory, Series A Top Cited Article 2005-2010").

  27. F. Blanchet-Sadri, "Primitive Partial Words." Discrete Applied Mathematics, Vol. 148, 2005, pp 195-213.

  28. L. Zhang and F. Blanchet-Sadri, "Algorithms for Approximate k-Covering of Strings." International Journal of Foundations of Computer Science, Vol. 16, No. 6, 2005, pp 1231-1251.

  29. F. Blanchet-Sadri and A.R. Anavekar, "Testing Primitivity on Partial Words." Discrete Applied Mathematics, Vol. 155, 2007, pp 279-287.

  30. F. Blanchet-Sadri and N.D. Wetzler, "Partial Words and the Critical Factorization Theorem Revisited." Theoretical Computer Science, Vol. 385, 2007, pp 179-192.

  31. F. Blanchet-Sadri, D. Bal and G. Sisodia, "Graph Connectivity, Partial Words, and a Theorem of Fine and Wilf." Information and Computation, Vol. 206, 2008, pp 676-693.

  32. F. Blanchet-Sadri, K. Corcoran, and J. Nyberg, "Periodicity Properties on Partial Words." Information and Computation, Vol. 206, 2008, pp 1057-1064.

  33. F. Blanchet-Sadri, L. Bromberg and K. Zipple, “Remarks on Two Nonstandard Versions of Periodicity in Words.” International Journal of Foundations of Computer Science, Vol. 19, No. 6, 2008, pp 1439-1448.

  34. F. Blanchet-Sadri, D. Blair and R.V. Lewis, "Equations on Partial Words." RAIRO-Theoretical Informatics and Applications, Vol. 43, 2009, pp 23-39.

  35. F. Blanchet-Sadri, R. Mercas and G. Scott, “A Generalization of Thue Freeness for Partial Words.” Theoretical Computer Science, Vol. 410, 2009, pp 793-800.

  36. F. Blanchet-Sadri, R. Jungers and J. Palumbo, “Testing Avoidability on Sets of Partial Words is Hard.” Theoretical Computer Science, Vol. 410, 2009, pp 968-972.

  37. F. Blanchet-Sadri, C.D. Davis, J. Dodge, R. Mercas and M. Moorefield, "Unbordered Partial Words." Discrete Applied Mathematics, Vol. 157, 2009, pp 890-900.

  38. F. Blanchet-Sadri, N.C. Brownstein, A. Kalcic, J. Palumbo and T. Weyand, “Unavoidable Sets of Partial Words.” Theory of Computing Systems, Vol. 45, No. 2, 2009, pp 381-406.

  39. F. Blanchet-Sadri and R. Mercas, “A Note on the Number of Squares in a Partial Word with One Hole.” RAIRO-Theoretical Informatics and Applications, Vol. 43, 2009, pp 767-774.

  40. F. Blanchet-Sadri, R. Mercas and G. Scott, “Counting Distinct Squares in Partial Words.” Acta Cybernetica, Vol. 19, 2009, pp 465-477.

  41. F. Blanchet-Sadri, E. Clader and O. Simpson, “Border Correlations of Partial Words.” Theory of Computing Systems, Vol. 47, No. 1, 2010, pp 179-195.

  42. F. Blanchet-Sadri, J. Fowler, J.D. Gafni and K.H. Wilson, “Combinatorics on Partial Word Correlations.” Journal of Combinatorial Theory, Series A, Vol. 117, 2010, pp 607-624.

  43. F. Blanchet-Sadri, T. Oey and T. Rankin, "Fine and Wilf's Theorem for Partial Words with Arbitrarily Many Weak Periods." International Journal of Foundations of Computer Science, Vol. 21, No. 5, 2010, pp 705-722.

  44. B. Blakeley, F. Blanchet-Sadri, J. Gunter and N. Rampersad, “On the Complexity of Deciding Avoidability of Sets of Partial Words.” Theoretical Computer Science, Vol. 411, 2010, pp 4263-4271.

  45. F. Blanchet-Sadri, R. Mercas, S. Simmons and E. Weissenstein, “Avoidable Binary Patterns in Partial Words.” Acta Informatica, Vol. 48, No. 1, 2011, pp 25-41 ("Erratum to: Avoidable Binary Patterns in Partial Words." Acta Informatica, Vol. 49, No. 1, 2012, pp 53-54).

  46. F. Blanchet-Sadri and J. Lensmire, “On Minimal Sturmian Partial Words.” Discrete Applied Mathematics, Vol. 159, No. 8, 2011, pp 733-745.

  47. F. Blanchet-Sadri, I. Choi and R. Mercas, “Avoiding Large Squares in Partial Words.” Theoretical Computer Science, Vol. 412, 2011, pp 3752-3758.

  48. F. Blanchet-Sadri, E. Allen, C. Byrum, M. Cucuringu and R. Mercas, “Counting Bordered Partial Words by Critical Positions.” The Electronic Journal of Combinatorics, Vol. 18, 2011, #P138.

  49. F. Blanchet-Sadri, J. I. Kim, R. Mercas, W. Severa, S. Simmons and D. Xu, “Avoiding Abelian Squares in Partial Words.” Journal of Combinatorial Theory, Series A, Vol. 119, 2012, pp 257-270.

  50. F. Blanchet-Sadri, S. Simmons and D. Xu, “Abelian Repetitions in Partial Words.” Advances in Applied Mathematics, Vol. 48, 2012, pp 194-214.

  51. F. Blanchet-Sadri and R. Mercas, “The Three-Squares Lemma for Partial Words with One Hole.” Theoretical Computer Science, Vol. 428, 2012, pp 1-9.

  52. F. Blanchet-Sadri, A. Chakarov, L. Manuelli, J. Schwartz and S. Stich, “Constructing Partial Words with Subword Complexities Not Achievable by Full Words.” Theoretical Computer Science, Vol. 432, 2012, pp 21-27.

  53. F. Blanchet-Sadri, B. Chen and A. Chakarov, “Number of Holes in Unavoidable Sets of Partial Words I.” Journal of Discrete Algorithms, Vol. 14, 2012, 55-64.

  54. F. Blanchet-Sadri, S. Ji and E. Reiland, “Number of Holes in Unavoidable Sets of Partial Words II.” Journal of Discrete Algorithms, Vol. 14, 2012, pp 65-73.

  55. F. Blanchet-Sadri, R. Mercas, A. Rashin and E. Willett, “Periodicity Algorithms and a Conjecture on Overlaps in Partial Words .” Theoretical Computer Science, Vol. 443, 2012, pp 35-45.

  56. F. Blanchet-Sadri, T. Mandel and G. Sisodia, “Periods in Partial Words: An Algorithm.” Journal of Discrete Algorithms, Vol. 16, 2012, pp 113-128.

  57. F. Blanchet-Sadri, “Algorithmic Combinatorics on Partial Words.” International Journal of Foundations of Computer Science, Vol. 23, No. 6, 2012, pp 1189-1206 (Invited paper).

  58. F. Blanchet-Sadri and S. Simmons, “Deciding Representability of Sets of Words of Equal Length.” Theoretical Computer Science, Vol. 475, 2013, pp 34-46.

  59. F. Blanchet-Sadri and N. Fox, “Abelian-Primitive Partial Words.” Theoretical Computer Science, Vol. 485, 2013, pp 16-37.

  60. F. Blanchet-Sadri, B. Chen and S. Munteanu, “A Note on Constructing Infinite Binary Words with Polynomial Subword Complexity.” RAIRO-Theoretical Informatics and Applications, Vol. 47, 2013, pp 195-199.

  61. F. Blanchet-Sadri, S. Simmons, A. Tebbe and A. Veprauskas, “Abelian Periods, Partial Words, and an Extension of a Theorem of Fine and Wilf.” RAIRO-Theoretical Informatics and Applications, Vol. 47, 2013, pp 215-234.

  62. F. Blanchet-Sadri and B. Woodhouse, “Strict Bounds for Pattern Avoidance.” Theoretical Computer Science, Vol. 506, 2013, pp 17-28.

  63. F. Blanchet-Sadri and S. Simmons, “Counting Minimal Semi-Sturmian Words.” Discrete Applied Mathematics, Vol. 161, 2013, pp 2851-2861.

  64. F. Blanchet-Sadri, A. Lohr and S. Scott, “Computing the Partial Word Avoidablity Indices of Binary Patterns.” Journal of Discrete Algorithms, Vol. 23, 2013, pp 113-118.

  65. F. Blanchet-Sadri, A. Lohr and S. Scott, “Computing the Partial Word Avoidablity Indices of Ternary Patterns.” Journal of Discrete Algorithms, Vol. 23, 2013, pp 119-142.

  66. F. Blanchet-Sadri, B. Chen and S. Munteanu, “Recurrence in Infinite Partial Words.” Theoretical Computer Science, Vol. 524, 2014, 41-47.

  67. F. Blanchet-Sadri, B. De Winkle and S. Simmons, “Abelian Pattern Avoidance in Partial Words.” RAIRO-Theoretical Informatics and Applications, to appear.

  68. F. Blanchet-Sadri, J. Currie, N. Fox and N. Rampersad, “Abelian Complexity of Fixed Point of Morphism 0 -> 012, 1 -> 02, 2 -> 1.” The Electronic Journal of Combinatorial Number Theory, to appear.

  69. F. Blanchet-Sadri, Y. Jiao, J. M. Machacek, J.D. Quigley and X. Zhang, “Squares in Partial Words.” Theoretical Computer Science, to appear.

  70. E. Balkanski, F. Blanchet-Sadri, M. Kilgore and B. J. Wyatt, “On the State Complexity of Partial Word DFAs.” Theoretical Computer Science, to appear.

  71. F. Blanchet-Sadri and M. Cucuringu, “Counting Primitive Partial Words.” Journal of Automata, Languages and Combinatorics, to appear.


Selected Refereed Conferences

  1. F. Blanchet-Sadri, D. Blair, and R.V. Lewis, "Equations on Partial Words." in R. Kralovic and P. Urzyczyn (Eds.), MFCS 2006, 31st International Symposium on Mathematical Foundations of Computer Science, August 28-September 1, 2006, Stara Lesna, Slovakia, Lecture Notes in Computer Science, Vol. 4162, Springer-Verlag, Berlin, Heidelberg, 2006, pp 167-178.

  2. F. Blanchet-Sadri, J.D. Gafni and K.H. Wilson, “Correlations of Partial Words.” in W. Thomas and P. Weil (Eds.), STACS 2007, 24th International Symposium on Theoretical Aspects of Computer Science, February 22-24, 2007, Aachen, Germany, Lecture Notes in Computer Science, Vol. 4393, Springer-Verlag, Berlin, Heidelberg, 2007, pp 97-108.

  3. F. Blanchet-Sadri, N.C. Brownstein and J. Palumbo, “Two Element Unavoidable Sets of Partial Words.” in T. Harju, J. Karhumäki, and A. Lepistö (Eds), DLT 2007, 11th International Conference on Developments in Language Theory, July 3-6, 2007, Turku, Finland, Lecture Notes in Computer Science, Vol. 4588, Springer-Verlag, Berlin, Heidelberg, 2007, pp 96-107.

  4. F. Blanchet-Sadri, K. Corcoran, and J. Nyberg, "Fine and Wilf's Periodicity Results on Partial Words and Consequences." in LATA 2007, 1st International Conference on Language and Automata Theory and Applications, March 29-April 4, 2007, Tarragona, Spain, GRLMC Report 35/07, pp 115-126.

  5. F. Blanchet-Sadri, T. Oey and T. Rankin, "Computing Weak Periods of Partial Words." in E. Csuhaj-Varju and Z. Esik (Eds.), AFL 2008, 12th International Conference on Automata and Formal Languages, May 27-30, 2008, Balatonfured, Hungary, Proceedings, pp 134-145.

  6. F. Blanchet-Sadri, R. Mercas and G. Scott, "Counting Distinct Squares in Partial Words." in E. Csuhaj-Varju and Z. Esik (Eds.), AFL 2008, 12th International Conference on Automata and Formal Languages, May 27-30, 2008, Balatonfured, Hungary, Proceedings, pp 122-133.

  7. F. Blanchet-Sadri, E. Allen, C. Byrum and R. Mercas, “How Many Holes Can an Unbordered Partial Word Contain?” in A.H. Dediu, A.M. Ionescu, and C. Martin-Vide (Eds.), LATA 2009, 3rd International Conference on Language and Automata Theory and Applications, April 2-8, 2009, Tarragona, Spain, Lecture Notes in Computer Science, Vol. 5457, Springer-Verlag, Berlin, Heidelberg, 2009, pp 176-187.

  8. F. Blanchet-Sadri, R. Mercas, A. Rashin and E. Willett, “An Answer to a Conjecture on Overlaps in Partial Words Using Periodicity Algorithms.” in A.H. Dediu, A.M. Ionescu and C. Martin-Vide (Eds.), LATA 2009, 3rd International Conference on Language and Automata Theory and Applications, April 2-8, 2009, Tarragona, Spain, Lecture Notes in Computer Science, Vol. 5457, Springer-Verlag, Berlin, Heidelberg, 2009, pp 188-199.

  9. B. Blakeley, F. Blanchet-Sadri, J. Gunter and N. Rampersad, "On the Complexity of Deciding Avoidability of Sets of Partial Words." in V. Diekert and D. Nowotka (Eds.), DLT 2009, 13th International Conference on Developments in Language Theory, June 30-July 3, 2009, Stuttgart, Germany, Lecture Notes in Computer Science, Vol. 5583, Springer-Verlag, Berlin, Heidelberg, 2009, pp 113-124.

  10. F. Blanchet-Sadri and B. Shirey, “Periods and Binary Partial Words.” in WORDS 2009, The 7th International Conference on Words, September 14-18, 2009, Salerno, Italy.

  11. F. Blanchet-Sadri, R. Mercas and K. Wetzler, “The Three-Squares Lemma for Partial Words with One Hole.” in WORDS 2009, The 7th International Conference on Words, September 14-18, 2009, Salerno, Italy.

  12. F. Blanchet-Sadri, J. I. Kim, R. Mercas, W. Severa and S. Simmons, “Abelian Square-Free Partial Words.” in A.-H. Dediu, H. Fernau and C. Martin-Vide (Eds.), LATA 2010, 4th International Conference on Language and Automata Theory and Applications, May 24-28, 2010, Trier, Germany, Lecture Notes in Computer Science, Vol. 6031, Springer-Verlag, Berlin, Heidelberg, 2010, pp 94-105.

  13. F. Blanchet-Sadri, R. Mercas, S. Simmons and E. Weissenstein, “Avoidable Binary Patterns in Partial Words.” in A.-H. Dediu, H. Fernau and C. Martin-Vide (Eds.), LATA 2010, 4th International Conference on Language and Automata Theory and Applications, May 24-28, 2010, Trier, Germany, Lecture Notes in Computer Science, Vol. 6031, Springer-Verlag, Berlin, Heidelberg, 2010, pp 106-117.

  14. F. Blanchet-Sadri, J. Schwartz, S. Stich and B. J. Wyatt, “Binary De Bruijn Partial Words with One Hole.” in J. Kratochvil et al. (Eds.), TAMC 2010, 7th Annual Conference on Theory and Applications of Models of Computation, June 7-11, 2010, Prague, Czech Republic, Lecture Notes in Computer Science, Vol. 6108, Springer-Verlag, Berlin, Heidelberg, 2010, pp 128-138.

  15. F. Blanchet-Sadri, A. Tebbe and A. Veprauskas, “Fine and Wilf's Theorem for Abelian Periods in Partial Words.” in JM 2010, 13iemes Journees Montoises d'Informatique Theorique, September 6-10, 2010, Amiens, France.

  16. F. Blanchet-Sadri, B. Chen and A. Chakarov, “Minimum Number of Holes in Unavoidable Sets of Partial Words of Size Three.” in C. S. Iliopoulos and W. F. Smyth (Eds.), IWOCA 2010, 21st International Workshop on Combinatorial Algorithms, July 26-28, 2010, London, United Kingdom, Lecture Notes in Computer Science, Vol. 6460, Springer-Verlag, Berlin, Heidelberg, 2011, pp 43-45.

  17. F. Blanchet-Sadri and J. Lensmire, “On Minimal Sturmian Partial Words.” in C. Durr and T. Schwentick (Eds.), STACS 2011, 28th International Symposium on Theoretical Aspects of Computer Science, March 10-12, 2011, Dortmund, Germany, LIPIcs 9 Schloss Dagstuhl-Leibniz-Zentrum fur Informatik, 2011, pp 225-236.

  18. F. Blanchet-Sadri, K. Black and A. Zemke, “Unary Pattern Avoidance in Partial Words Dense with Holes.” in A.-H. Dediu, S. Inenaga and C. Martin-Vide (Eds.), LATA 2011, 5th International Conference on Language and Automata Theory and Applications, May 26-31, 2011, Tarragona, Spain, Lecture Notes in Computer Science, Vol. 6638, Springer-Verlag, Berlin, Heidelberg, 2011, pp 155-166.

  19. F. Blanchet-Sadri and S. Simmons, "Avoiding Abelian Powers in Partial Words." in G. Mauri and A. Leporati (Eds.), DLT 2011, 15th International Conference on Developments in Language Theory, July 19-22, 2011, Milano, Italy, Lecture Notes in Computer Science, Vol. 6795, Springer-Verlag, Berlin, Heidelberg, 2011, pp 70-81.

  20. F. Blanchet-Sadri, S. Nelson and A. Tebbe, “On Operations Preserving Primitivity of Partial Words with One Hole.” in P. Domosi and Sz. Ivan (Eds.), AFL 2011, 13th International Conference on Automata and Formal Languages, August 17-22, 2011, Debrecen, Hungary, Proceedings, pp 93-107.

  21. F. Blanchet-Sadri, “Open Problems on Avoidable Patterns in Partial Words.” in P. Domosi and Sz. Ivan (Eds.), AFL 2011, 13th International Conference on Automata and Formal Languages, August 17-22, 2011, Debrecen, Hungary, Proceedings, pp 12-24 (Invited paper).

  22. F. Blanchet-Sadri, T. Mandel and G. Sisodia, “Periods in Partial Words: An Algorithm.” in C. S. Iliopoulos and W. F. Smyth (Eds.), IWOCA 2011, 22nd International Workshop on Combinatorial Algorithms, June 20-22, 2011, Victoria, British Columbia, Canada, Lecture Notes in Computer Science, Vol. 7056, Springer-Verlag, Berlin, Heidelberg, 2011, pp 57-70.

  23. F. Blanchet-Sadri, A. Chakarov, L. Manuelli, J. Schwartz and S. Stich, “Recurrent Partial Words.” in P. Ambroz, S. Holub and Z. Masakova (Eds.), WORDS 2011, 8th International Conference on Words, September 12-16, 2011, Prague, Czech Republic, Electronic Proceedings of Theoretical Computer Science, Vol. 63, 2011, pp 71-82.

  24. F. Blanchet-Sadri and S. Simmons, “Deciding Representability of Sets of Words of Equal Length.” in M. Kutrib, N. Moreira and R. Reis (Eds.), DCFS 2012, 14th International Workshop on Descriptional Complexity of Formal Systems, July 23-25, 2012, Braga, Portugal, Lecture Notes in Computer Science, Vol. 7386, Springer-Verlag, Berlin, Heidelberg, 2012, pp 103-116.

  25. F. Blanchet-Sadri, Y. Jiao and J. Machacek, “Squares in Binary Partial Words.” in H.-C. Yen and O. H. Ibarra (Eds.), DLT 2012, 16th International Conference on Developments in Language Theory, August 14-17, 2012, Taipei, Taiwan, Lecture Notes in Computer Science, Vol. 7410, Springer-Verlag, Berlin, Heidelberg, 2012, pp 404-415.

  26. F. Blanchet-Sadri and S. Simmons, “Abelian Pattern Avoidance in Partial Words.” in B. Rovan, V. Sassone and P. Widmayer (Eds.), MFCS 2012, 37th International Symposium on Mathematical Foundations of Computer Science, August 27-31, 2012, Bratislava, Slovakia, Lecture Notes in Computer Science, Vol. 7464, Springer-Verlag, Berlin, Heidelberg, 2012, pp 210-221.

  27. F. Blanchet-Sadri, D. Allums, J. Lensmire and B. J. Wyatt, “Constructing Minimal Partial Words of Maximum Subword Complexity.” in JM 2012, 14th Mons Days of Theoretical Computer Science, September 11-14, 2012, Universite catholique de Louvain, Belgium.

  28. F. Blanchet-Sadri, A. Lohr and S. Scott, “Computing the Partial Word Avoidablity Indices of Ternary Patterns.” in S. Arumugam and B. Smyth (Eds.), IWOCA 2012, 23rd International Workshop on Combinatorial Algorithms, July 19-21, 2012, Tamil Nadu, India, Lecture Notes in Computer Science, Vol. 7643, Springer-Verlag, Berlin, Heidelberg, 2012, pp 206-218.

  29. F. Blanchet-Sadri and J. Lazarow, “Suffix Trees for Partial Words and the Longest Common Compatible Prefix Problem.” in A.-H. Dediu, C. Martin-Vide and B. Truthe (Eds.), LATA 2013, 7th International Conference on Language and Automata Theory and Applications, April 2-5, 2013, Bilbao, Spain, Lecture Notes in Computer Science, Vol. 7810, Springer-Verlag, Berlin, Heidelberg, 2013, pp 165--176.

  30. F. Blanchet-Sadri, M. Bodnar, N. Fox and J. Hidakatsu, “A Graph Polynomial Approach to Primitivity.” in A.-H. Dediu, C. Martin-Vide and B. Truthe (Eds.), LATA 2013, 7th International Conference on Language and Automata Theory and Applications, April 2-5, 2013, Bilbao, Spain, Lecture Notes in Computer Science, Vol. 7810, Springer-Verlag, Berlin, Heidelberg, 2013, pp 153-164.

  31. F. Blanchet-Sadri and B. Woodhouse, “Strict Bounds for Pattern Avoidance.” in M.-P. Beal and O. Carton (Eds.), DLT 2013, 17th International Conference on Developments in Language Theory, June 18-21, 2013, Paris-Est, France, Lecture Notes in Computer Science, Vol. 7907, Springer-Verlag, Berlin, Heidelberg, 2013, pp 106-117.

  32. F. Blanchet-Sadri and N. Fox, “On the Asymptotic Abelian Complexity of Morphic Words.” in M.-P. Beal and O. Carton (Eds.), DLT 2013, 17th International Conference on Developments in Language Theory, June 18-21, 2013, Paris-Est, France, Lecture Notes in Computer Science, Vol. 7907, Springer-Verlag, Berlin, Heidelberg, 2013, pp 94-105.

  33. E. Balkanski, F. Blanchet-Sadri, M. Kilgore and B. J. Wyatt, “Partial Word DFAs.” in S. Konstantinidis (Ed.), CIAA 2013, 18th International Conference on Implementation and Application of Automata, July 16-19, 2013, Halifax, Nova Scotia, Canada, Lecture Notes in Computer Science, Vol. 7982, Springer-Verlag, Berlin, Heidelberg, 2013, pp 36-47 (Awarded ``Best Paper Award of CIAA 2013'').

  34. F. Blanchet-Sadri and S. Munteanu, “Deciding Representability of Sets of Words of Equal Length in Polynomial Time.” in T. Lecroq and L. Mouchard (Eds.), IWOCA 2013, 24th International Workshop on Combinatorial Algorithms, July 10-12, 2013, Rouen, France, Lecture Notes in Computer Science, Vol. 8288, Springer-Verlag, Berlin, Heidelberg, 2013, pp 28-40.

  35. F. Blanchet-Sadri, A. Lohr, S. Simmons and B. Woodhouse, “Computing Depths of Patterns.” in A.-H. Dediu, C. Martin-Vide, J.-L. Sierra-Rodriguez and B. Truthe (Eds.), LATA 2014, 8th International Conference on Language and Automata Theory and Applications, March 10-14, 2014, Madrid, Spain, Lecture Notes in Computer Science, Vol. 8370, Springer-Verlag, Berlin, Heidelberg, 2014, pp 173-185.

  36. F. Blanchet-Sadri, M. Bodnar and B. De Winkle, “New Bounds and Extended Relations Between Prefix Arrays, Border Arrays, Undirected Graphs, and Indeterminate Strings.” in E. W. Mayr and N. Portier (Eds.), STACS 2014, 31st International Symposium on Theoretical Aspects of Computer Science, March 5-8, 2014, Lyon, France, LIPIcs Schloss Dagstuhl-Leibniz-Zentrum fur Informatik, Vol. 25, 2014, pp 162-173.



Selected Talks



Selected Research Grants


REU Site: Algorithmic Combinatorics on Words 2011-2014

NSF (Individual), National Science Foundation (DMS Division of Mathematical Sciences), 2011-2014.

PROJECT SUMMARY

This “Research Experiences for Undergraduates (REU)” project entitled Algorithmic Combinatorics on Words 2011-2014 involves students at the crossroads between Mathematics and Computer Science. Words, or sequences of symbols over a finite alphabet, are natural objects in several research areas including group theory, number theory, automata and formal language theory, coding theory, and theory of algorithms. This project will provide unique opportunities for summer research for ten students per year for an eight-week period each year.

The five goals or objectives for student activities are: A first objective of this interdisciplinary project is to investigate challenging problems of current interest related to partial words, or sequences that may have some undefined positions. Research topics include computing bounds on the lengths of de Bruijn partial words, counting the number of distinct squares in partial words, and constructing abelian repetition-free partial words. Combinatorics on partial words is a promising line of research that has practical uses in several areas, notably in molecular biology and bio-inspired computing, as well as in the design of a new generation of pattern matching algorithms. Two types of research opportunities will be emphasized:

  1. computer related research, with students writing programs to perform experiments on partial words and to implement algorithms; and
  2. combinatorics related research, with students investigating properties of partial words to generate conjectures, to prove theorems, and to discover algorithms.

While achieving this objective, a second objective of the project is for students to develop superior skills in mathematical writing and oral communication. A third objective of this project is to submit the resulting original and high quality research on algorithmic combinatorics on words done with undergraduate students to leading journals and to encourage them to present it at national/international meetings or conferences. A fourth objective is for students to gain experience in the use of computers and their interaction in mathematical research. In addition, students will establish World Wide Web server interfaces for automated use of the programs related to the discovered combinatorial algorithms. Although student participants will be selected based on merit after a nationwide recruitment from a broad range of colleges and universities, a fifth objective of the project is to encourage the participation of underrepresented groups including women, minorities, and persons with disabilities. As a result of taking part in this project, students will get motivated and will become better prepared to pursue advanced degree programs in mathematical sciences.




REU Site: Algorithmic Combinatorics on Words 2008-2011

NSF (Individual), National Science Foundation (DMS Division of Mathematical Sciences), 2008-2011.



REU Site: Algorithmic Combinatorics on Words

NSF (Individual), National Science Foundation (DMS Division of Mathematical Sciences), 2005-2008.



Computing Patterns in Strings

NSF (Individual), National Science Foundation (75% RUI Theory of Computing and 25% RUI Algebra, Number Theory, and Combinatorics), 2002-2005.

PROJECT SUMMARY

The problem of computing patterns in sequences or strings of characters from a finite alphabet has important applications in numerous areas of computer science, notably in data compression, information theory, and pattern matching. This problem has also important applications in biology. The stimulus for such recent works is the study of biological sequences such as DNA and protein that play a central role in molecular biology. DNA sequences can be viewed as quite long but finite strings of nucleotides of 4 different types, while protein sequences can be viewed as finite strings of amino acids of 20 possible types. Patterns such as periodicities and repetitions make up a significant fraction of both DNA and protein sequences. Although the functions of these patterns are not well understood, they appear important for understanding the expression, regulation and evolution of a biological sequence. These patterns can be used to identify the sequence among other sequences, an application that plays a role in genetic fingerprinting. Repetitions in biological sequences have been associated with human genetic diseases. They also complicate multiple sequence alignment because matches may be present in numerous places.

The literature has generally considered problems in which a period u of a repetition is invariant. It has been required that occurrences of u match each other exactly. Due to the action of evolutionary mutation, patterns in biological strings are seldom exact but rather approximate. It therefore becomes necessary to recognize u' as an occurence of u if the distance between u' and u is bounded by a certain threshold. Several definitions of distance have been proposed like the Hamming distance which counts the minimum number of character substitutions required to transform u' into u, and the edit distance which counts the minimum number of substitutions, insertions, and deletions of characters required to transform u' into u. Although there is an enormous literature dealing with approximate pattern matching according to these and other definitions of distance, very little is known on approximate repetitions, a version of repetitions where errors are allowed, and much remains to be done.

Given the importance of patterns in biological strings and the exponential growth in the size of the DNA database, it is important to develop efficient methods for detecting these patterns. This project studies patterns such as periodicities, repetitions, covers, and seeds and their approximate versions built upon various commonly used distance measures. It is natural to consider approximate string matching techniques when developing algorithms for approximate patterns. Techniques that might prove useful include recent combinatorial techniques related to partial strings which are strings where a number of gap characters are allowed. Techniques also include the cover array, the highest scoring paths in weighted grid graphs, the probabilistic models that have been proposed for repetitions, and the subtree max gap problem which seems to be a powerful tool in parallel algorithm design. Several students, undergraduate and graduate, will be involved in different aspects of this project.



Decipherability of Codes and Applications

NSF (Individual), National Science Foundation (RUI Theory of Computing), 1997-2000.



Equations on Varieties of Monoids

NSF (Individual), National Science Foundation (RUI Theory of Computing), 1993-1996.



The Decidability Problem of the Dot-Depth Hierarchy

NSF (Individual), National Science Foundation (RUI Theory of Computing), 1991-1993.

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