Bisimilarity is not Borel

We prove that the relation of bisimilarity between countable labelled transition systems is $\Sigma_1^1$-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it. This has an impact on the theory of probabilistic and nondeterministic processes over uncountable spaces, since logical characterizations of bisimilarity (as, for instance, those based on the unique structure theorem for analytic spaces) require a countable logic whose formulas have measurable semantics. Our reduction shows that such a logic does not exist in the case of image-infinite processes.Comment: 20 pages, 1 figure; proof of Sigma_1^1 completeness added with extended comments. I acknowledge careful reading by the referees. Major changes in Introduction, Conclusion, and motivation for NLMP. Proof for Lemma 22 added, simpler proofs for Lemma 17 and Theorem 30. Added references. Part of this work was presented at Dagstuhl Seminar 12411 on Coalgebraic Logic

Semipullbacks of labelled Markov processes

A 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 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 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 Doberkat (extending a result by 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 "semipullback"). In this paper, we extend the previous 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.Comment: 10 pages; v2: missing attribution to Doberka

The Lattice of Congruences of a Finite Line Frame

Let $\mathbf{F}=\left\langle F,R\right\rangle$ be a finite Kripke frame. A congruence of $\mathbf{F}$ is a bisimulation of $\mathbf{F}$ that is also an equivalence relation on F. The set of all congruences of $\mathbf{F}$ is a lattice under the inclusion ordering. In this article we investigate this lattice in the case that $\mathbf{F}$ is a finite line frame. We give concrete descriptions of the join and meet of two congruences with a nontrivial upper bound. Through these descriptions we show that for every nontrivial congruence $\rho$, the interval $[\mathrm{Id_{F},\rho]}$ embeds into the lattice of divisors of a suitable positive integer. We also prove that any two congruences with a nontrivial upper bound permute.Comment: 31 pages, 11 figures. Expanded intro, conclusions rewritten. New, less geometrical, proofs of Lemma 19 and (former) Lemma 3

Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids

We study varieties with a term-definable poset structure, "po-groupoids". It is known that connected posets have the "strict refinement property" (SRP). In [arXiv:0808.1860v1 [math.LO]] it is proved that semidegenerate varieties with the SRP have definable factor congruences and if the similarity type is finite, directly indecomposables are axiomatizable by a set of first-order sentences. We obtain such a set for semidegenerate varieties of connected po-groupoids and show its quantifier complexity is bounded in general

Encapsulation and subsequent freeze-drying of Lactobacillus reuteri CRL 1324 for its potential inclusion in vaginal probiotic formulations

Probiotic formulations must include a high number of viable and active microorganisms. In this work, the survival of human vaginal Lactobacillus reuteri CRL 1324 during encapsulation, lyophilization and storage, and the activity of encapsulated and/or freeze-dried bacterial cells were evaluated. Extrusion-ionic gelation technique was applied to encapsulate L. reuteri CRL 1324, using xanthan and gellan. Encapsulated and free bacterial cells were freeze-dried with or without lactose and skim milk as lyoprotectors. The different systems obtained were stored at room temperature and at 4°C for 150 days. The following determinations were performed: L. reuteri CRL 1324 viability, microorganism released from capsules, survival in a medium simulating the vaginal fluid and maintenance of beneficial properties (growth inhibition of opportunistic pathogenic Streptococcus agalactiae NH 17 and biofilm formation). L. reuteri CRL 1324 encapsulation was efficient, allowing the recovery of a high number of entrapped lactobacilli. The survival of encapsulated L. reuteri during lyophilization and storage was significantly higher in the presence of lyoprotectors. At the end of storage, highest numbers of viable cells were obtained in free or encapsulated cells freeze-dried with lyoprotectors, stored at 4°C. Encapsulated and/or liophilized L. reuteri cells maintained their viability in simulated vaginal fluid as well as the ability to inhibit S. agalactiae NH 17 growth and to form biofilm. Encapsulated and freeze-dried L. reuteri CRL 1324 can be included in a suitable pharmaceutical form for vaginal application to prevent or treat urogenital infections in women.Fil: Juárez Tomás, María Silvina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucuman. Centro de Referencia Para Lactobacilos; ArgentinaFil: de Gregorio, Priscilla Romina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucuman. Centro de Referencia Para Lactobacilos; ArgentinaFil: Leccese Terraf, Maria Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucuman. Centro de Referencia Para Lactobacilos; ArgentinaFil: Nader, Maria Elena Fatima. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucuman. Centro de Referencia Para Lactobacilos; Argentin