In this talk I will first give an introduction about using non-commutative group theory in cryptography. In particular, I will present a couple of non-commutative public key cryptosystems, one using polycyclic groups and one using matrices over group-rings.
The talk will be in English.It is well-known that any finite R-trivial monoid can be embedded into the monoid of all extensive transformations of the n-element chain for an appropriate positive integer n. Thus, such monoids can be conveniently considered as monoids of row-monomial upper-triangular matrices of order n over the trivial group with zero adjoined. We generalize this result by showing that any finite monoid on which Green's relations R and H coincide divides the monoid of all row-monomial upper-triangular matrices of order n over some group G with zero adjoined. The group G and the order n are given constructively.
The talk will be given in English.In earlier work we gave a game-based semantics for checkonly QVT-R transformations. We restricted so-called "when" and "where" clauses, parts of the relation definition, to be conjunctions of relation invocations only, and like the OMG standard, we did not consider cases in which a relation might (directly or indirectly) invoke itself recursively.
In this work we show how to interpret checkonly QVT-R - or any future model transformation language structured similarly - in the mu-calculus and use its well-understood model-checking game to lift these restrictions. The interpretation via fixpoints gives a principled argument for assigning semantics to recursive transformations. We demonstrate that a particular class of recursive transformations must be ruled out due to monotonicity considerations. We demonstrate and justify a corresponding extension to the rules of the QVT-R game.
Starting at 4 p.m., coffee and tea will be served in front of the lecture hall "Felix Klein". You are welcome.
Wir geben eine Übersicht über Ergebnisse zur Duplikation als Operation auf Formalen Sprachen, insbesondere regulären Sprachen. Abhänging von der Größe des Alphabets und der maximalen Länge der verdoppelten Faktoren wird Regularität zum Teil erhalten, zum Teil nicht. Weiterhin betrachten wir die Umkehrung der Duplikation, also die Reduzierung von Quadraten, ebenfalls als Stringoperation.
"Given an interpretation of function symbols of a ranked signature by
linear functions, compute efficiently the interpretations of a set of
terms (containing variables)."
The computations are symbolic in the sense that all coefficients are
represented by expressions that involve unknowns, and a constraint
solver is used to compute their actual values. Here, we are not
concerned with the solving, but just want to ensure that the
constraint program is short.
One approximative solution of the compression problem is described in
[1, Section 7.4], and is implemented in the termination prover
Matchbox, (compressor source code is now available separately from
[3]). It is equivalent to a greedy construction of a linear acyclic
context free tree grammar in Chomsky normal form [2].
In the talk, we describe this connection, give some data, and discuss
extensions.
[1] Jörg Endrullis, Johannes Waldmann, Hans Zantema:
Matrix Interpretations for Proving Termination of Term Rewriting.
J. Autom. Reasoning 40(2-3): 195-220 (2008)
[2] Markus Lohrey, Sebastian Maneth, Manfred Schmidt-Schauß:
Parameter Reduction in Grammar-Compressed Trees.
FOSSACS 2009: 212-226
[3] http://dfa.imn.htwk-leipzig.de/cgi-bin/gitweb.cgi?p=tpdb.git;a=blob;f=TPDB/Compress.hs;hb=HEAD
This is joint work with Manfred Droste.
This is joint work with Stefan Göller.
Joint work with Rüdiger Göbel (Essen)
(Joint work with Niko Haubold and Markus Lohrey)