Aleksi Saarela

Information

I am a researcher of mathematics in the University of Turku. My email address is of the form firstname.lastname@utu.fi. There is some personal information about me in Finnish and a resume (pdf).


Teaching

I will teach the course Algebraic Structures in Cryptography in Fall 2017 and I am responsible for the self-study course Selected Topics in Cryptography.


Research

My research area is discrete mathematics, or more precisely combinatorics on words. My publications are listed below and in the list of publications (pdf) in a different order. I have a Google Scholar Citations page.


Publications

To appear

(A.28) Saarela, Aleksi:
Palindromic length in free monoids and free groups.
Proceedings of the 11th WORDS (To appear)

2017

(A.27) Cassaigne, Julien and Karhumäki, Juhani and Saarela, Aleksi:
On growth and fluctuation of k-abelian complexity.
European J. Combin., 65:92-105 (2017) (pdf) (link)

(D.02) Karhumäki, Juhani and Matiyasevich, Yuri and Saarela, Aleksi (editors):
Proceedings of the Fourth Russian Finnish Symposium on Discrete Mathematics.
TUCS Lecture Notes 26 (2017)

(B.04) Karhumäki, Juhani and Saarela, Aleksi and Zamboni, Luca Q.:
Variations of the Morse-Hedlund theorem for k-abelian equivalence.
Acta Cybernet., 23(1):175-189 (2017) (pdf) (link)

(A.26) Saarela, Aleksi:
Word equations where a power equals a product of powers.
Proceedings of the 34th STACS, LIPIcs 66:55:1-55:9, Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik (2017) (pdf) (link)

2016

(A.25) Nowotka, Dirk and Saarela, Aleksi:
A connection between one-unknown word equations and constant-free three-unknown word equations.
Proceedings of the 20th DLT, LNCS 9840:332-343, Springer (2016) (pdf) (link)

(A.24) Endrullis, Jörg and Karhumäki, Juhani and Klop, Jan Willem and Saarela, Aleksi:
Degrees of infinite words, polynomials and atoms.
Proceedings of the 20th DLT, LNCS 9840:164-176, Springer (2016) (pdf) (link)

(A.23) Saarela, Aleksi:
Equivalence relations defined by numbers of occurrences of factors.
Fund. Inform., 145(3):385-397 (2016) (pdf) (link)

(D.01) Karhumäki, Juhani and Saarela, Aleksi (editors):
Proceedings of the Finnish Mathematical Days 2016.
TUCS Lecture Notes 25 (2016)

(I.02) Saarela, Aleksi:
k-abelian complexity and fluctuation.
Video presentation in the workshop ``Combinatorics on Words'' at CIRM (2016) (link)

2015

(B.03) Endrullis, Jörg and Klop, Jan Willem and Saarela, Aleksi and Whiteland, Markus:
Degrees of transducibility.
Proceedings of the 10th WORDS, LNCS 9304:1-13, Springer (2015) (pdf) (link) (Related to an invited talk given by J. Endrullis)

(A.22) Cassaigne, Julien and Karhumäki, Juhani and Saarela, Aleksi:
On growth and fluctuation of k-abelian complexity.
Proceedings of the 10th CSR, LNCS 9139:109-122, Springer (2015) (pdf) (link) (Journal version in A.27)

(A.21) Saarela, Aleksi:
Systems of word equations, polynomials and linear algebra: A new approach.
European J. Combin., 47:1-14 (2015) (pdf) (link)

2014

(A.20) Mercas, Robert and Saarela, Aleksi:
5-abelian cubes are avoidable on binary alphabets.
RAIRO Inform. Theor. Appl., 48(4):467-478 (2014) (pdf) (link)

(B.02) Saarela, Aleksi:
Equivalence relations defined by numbers of occurrences of factors.
Proceedings of the 3rd RuFiDiM (2014) (Journal version in A.23)

(A.19) Karhumäki, Juhani and Saarela, Aleksi and Zamboni, Luca Q.:
Variations of the Morse-Hedlund theorem for k-abelian equivalence.
Proceedings of the 18th DLT, LNCS 8633:203-214, Springer (2014) (pdf) (link) (Journal version in B.04)

(I.01) Saarela, Aleksi:
Äärettömät sanat.
Video presentation at the Academy Club for Young Scientists, organized by the Finnish Academy of Science and Letters (2014) (link)

2013

(A.18) Karhumäki, Juhani and Puzynina, Svetlana and Saarela, Aleksi:
Fine and Wilf's theorem for k-abelian periods.
Internat. J. Found. Comput. Sci., 24(7):1135-1152 (2013) (pdf) (link)

(A.17) Karhumäki, Juhani and Saarela, Aleksi and Zamboni, Luca Q.:
On a generalization of Abelian equivalence and complexity of infinite words.
J. Combin. Theory Ser. A, 120(8):2189-2206 (2013) (pdf) (link)

(A.16) Saarela, Aleksi:
Weakly unambiguous morphisms with respect to sets of patterns with constants.
Proceedings of the 9th WORDS, LNCS 8079:229-237, Springer (2013) (pdf) (link)

(A.15) Huova, Mari and Saarela, Aleksi:
Strongly k-abelian repetitions.
Proceedings of the 9th WORDS, LNCS 8079:161-168, Springer (2013) (pdf) (link)

(A.14) Mercas, Robert and Saarela, Aleksi:
3-abelian cubes are avoidable on binary alphabets.
Proceedings of the 17th DLT, LNCS 7907:374-383, Springer (2013) (pdf) (link)

2012

(B.01) Mercas, Robert and Saarela, Aleksi:
5-abelian cubes are avoidable on binary alphabets.
Proceedings of the 14th Mons Days (2012) (pdf) (Journal version in A.20)

(A.13) Huova, Mari and Karhumäki, Juhani and Saarela, Aleksi:
Problems in between words and abelian words: k-abelian avoidability.
Theoret. Comput. Sci., 454:172-177 (2012) (pdf) (link)

(A.12) Karhumäki, Juhani and Puzynina, Svetlana and Saarela, Aleksi:
Fine and Wilf's theorem for k-abelian periods.
Proceedings of the 16th DLT, LNCS 7410:296-307, Springer (2012) (pdf) (link) (Journal version in A.18)

(G.03) Saarela, Aleksi:
Word equations and related topics: independence, decidability and characterizations.
Doctoral dissertation, University of Turku (2012) (pdf) (link) (Based on A.01, A.04, A.08, A.09, A.10 and A.11)

2011

(A.11) Karhumäki, Juhani and Saarela, Aleksi:
The unique decipherability in the monoid of regular languages is undecidable.
Fund. Inform., 110(1-4):197-200 (2011) (pdf) (link)

(A.10) Saarela, Aleksi:
Systems of word equations and polynomials: a new approach.
Proceedings of the 8th WORDS, EPTCS 63:215-225 (2011) (pdf) (link) (Journal version in A.21)

(A.09) Karhumäki, Juhani and Saarela, Aleksi:
On maximal chains of systems of word equations.
Proc. Steklov Inst. Math., 274:116-123 (2011) (pdf) (link)

(A.08) Saarela, Aleksi:
Unique decipherability in the additive monoid of sets of numbers.
RAIRO Inform. Theor. Appl., 45(2):225-234 (2011) (pdf) (link)

(A.07) Huova, Mari and Karhumäki, Juhani and Saarela, Aleksi and Saari, Kalle:
Local squares, periodicity and finite automata.
In Calude, Cristian and Rozenberg, Grzegorz and Salomaa, Arto (editors), Rainbow of Computer Science, LNCS 6570:90-101, Springer (2011) (pdf) (link)

2010

(A.06) Karhumäki, Juhani and Saarela, Aleksi:
Noneffective regularity of equality languages and bounded delay morphisms.
Discrete Math. Theor. Comput. Sci., 12(4):9-18 (2010) (pdf) (link)

2009

(A.05) Saarela, Aleksi:
Ultimately constant abelian complexity of infinite words.
J. Autom. Lang. Comb., 14(3-4):255-258 (2009) (pdf) (link)

(A.04) Saarela, Aleksi:
On the complexity of Hmelevskii's theorem and satisfiability of three unknown equations.
Proceedings of the 13th DLT, LNCS 5583:443-453, Springer (2009) (pdf) (link)

(A.03) Karhumäki, Juhani and Saarela, Aleksi:
Noneffective regularity of equality languages and bounded delay morphisms.
Proceedings of the conference AutoMathA 2009 (2009) (pdf) (Journal version in A.06)

(G.02) Saarela, Aleksi:
A new proof of Hmelevskii's theorem.
Licentiate thesis, University of Turku (2009) (pdf)

2008

(A.02) Saarela, Aleksi and Ekberg, Jan-Erik and Nyberg, Kaisa:
Random beacon for privacy and group security.
Proceedings of the 4th IEEE International Conference on Wireless and Mobile Computing, Networking and Communications, 514-519 (2008) (pdf) (link)

(A.01) Karhumäki, Juhani and Saarela, Aleksi:
An analysis and a reproof of Hmelevskii's theorem.
Proceedings of the 12th DLT, LNCS 5257:467-478, Springer (2008) (pdf) (link)

2007

(G.01) Saarela, Aleksi:
Sanayhtälöiden parametriset ratkaisut.
Master's thesis, University of Turku (2007) (pdf)