## Current graduate students

• Martín Moroni
• Mauricio Tellechea (Assistant Professor)
• Pablo Ventura

## Recent Papers (and latest manuscripts)

1. M. Badano and D. Vaggione, “Characterization of context-free languages,” Theor. Comput. Sci. 676: 92-96 (2017).
[ BibTeX ]
@article{zbMATH06714282,
author = {M. {Badano} and D. {Vaggione}},
title = {{Characterization of context-free languages}},
fjournal = {{Theoretical Computer Science}},
journal = {{Theor. Comput. Sci.}},
issn = {0304-3975},
volume = {676},
pages = {92--96},
year = {2017},
publisher = {Elsevier, Amsterdam},
language = {English},
doi = {10.1016/j.tcs.2017.03.002},
msc2010 = {68Q}
}

2. M. Badano and D. Vaggione, “$\mathcal{V}_{SI}$ first order implies $\mathcal{V}_{DI}$ first order,” Acta Math. Hung. 151 (1): 47-49 (2017).
[ BibTeX ]
@article{zbMATH06707836,
author = {M. {Badano} and D. {Vaggione}},
title = {{$\mathcal{V}_{SI}$ first order implies $\mathcal{V}_{DI}$ first order}},
fjournal = {{Acta Mathematica Hungarica}},
journal = {{Acta Math. Hung.}},
issn = {0236-5294; 1588-2632/e},
volume = {151},
number = {1},
pages = {47--49},
year = {2017},
publisher = {Springer Netherlands, Dordrecht; Akad\'emiai Kiad\'o, Budapest},
language = {English},
doi = {10.1007/s10474-016-0676-0},
msc2010 = {08B10}
}

3. M. V. Badano and D. J. Vaggione, “Varieties with equationally definable factor congruences II,” Algebra Univers. (2017).
[ BibTeX ]
@article{edfc2,
author = {Mariana V. {Badano} and Diego J. {Vaggione}},
title = {{Varieties with equationally definable factor congruences II}},
fjournal = {{Algebra Universalis}},
journal = {{Algebra Univers.}},
issn = {0002-5240; 1420-8911/e},
year = {2017},
publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
language = {English},
note = {In press},
msc2010 = {03C05 08B05 08B10}
}

4. J. Pachl and P. Sánchez Terraf, “Semipullbacks of labelled Markov processes,” arXiv:1706.02801 (2017).
[ arXiv | Abstract | BibTeX ]

A \emph{labelled Markov process (LMP)} consists of a measurable space $S$ together with an indexed family of Markov kernels from $S$ to itself. This structure has been used to model probabilistic computations in Computer Science, and one of the main problems in the area is to define and decide whether two LMP $S$ and $S’$ “behave the same”. There are two natural categorical definitions of sameness of behavior: $S$ and $S’$ are \emph{bisimilar} if there exist an LMP $T$ and measure preserving maps forming a diagram of the shape $S\leftarrow T \rightarrow{S’}$; and they are \emph{behaviorally equivalent} if there exist some $U$ and maps forming a dual diagram $S\rightarrow U \leftarrow{S’}$. These two notions differ for general measurable spaces but Edalat proved that they coincide for analytic Borel spaces, showing that from every diagram $S\rightarrow U \leftarrow{S’}$ one can obtain a bisimilarity diagram as above. Moreover, the resulting square of measure preserving maps is commutative (a \emph{semipullback}). In this paper, we extend Edalat’s result to measurable spaces $S$ isomorphic to a universally measurable subset of a Polish space with the trace of the Borel $\sigma$-algebra, using a version of Strassen’s theorem on common extensions of finitely additive measures.

@article{2017arXiv170602801P,
author = {Pachl, Jan and S{\'a}nchez Terraf, Pedro},
title = {Semipullbacks of labelled {M}arkov processes},
journal = {ArXiv e-prints},
archiveprefix = {arXiv},
eprint = {1706.02801},
primaryclass = {math.PR},
keywords = {Mathematics - Probability, Computer Science - Logic in Computer Science, 28A35, 28A60, 68Q85, F.4.1, F.1.2},
year = 2017,
month = jun,
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
abstract = {A \emph{labelled Markov process (LMP)} consists of a measurable
space $S$ together with an indexed family of Markov kernels from $S$
to itself. This structure has been used to model probabilistic
computations in Computer Science, and one of the main problems in
the area is to define and decide whether two LMP $S$ and $S'$ behave
the same''. There are two natural categorical definitions of
sameness of behavior: $S$ and $S'$ are \emph{bisimilar}
if there exist an LMP $T$ and measure preserving maps
forming a diagram of the shape
$S\leftarrow T \rightarrow{S'}$; and they
are \emph{behaviorally equivalent}
if there exist some $U$ and maps forming a dual diagram
$S\rightarrow U \leftarrow{S'}$.
These two notions differ for general measurable spaces but Edalat
proved that they coincide for analytic Borel spaces, showing that
from every
diagram $S\rightarrow U \leftarrow{S'}$ one can obtain a
bisimilarity diagram as above. Moreover, the resulting square of
measure preserving maps is commutative (a \emph{semipullback}).
In this paper, we extend Edalat's result to measurable spaces $S$
isomorphic to a universally measurable subset of
a Polish space with the trace of the Borel $\sigma$-algebra, using a
version of Strassen's theorem on
common extensions of finitely additive measures.}
}