## Research team

- Diego Vaggione (Head of the group and Full Professor)
- Hector Gramaglia (Associate Professor)
- Miguel Campercholi (Adjunct Professor and Conicet Researcher)
- Pedro Sánchez Terraf (Adjunct Professor and Conicet Researcher)
- Mariana Badano (Assistant Professor and Postdoctoral fellow)

## Current graduate students

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

## Recent Papers (and latest manuscripts)

- 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} }`

- 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} }`

- 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} }`

- 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, adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170602801P}, 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.} }`