Restricted Space Algorithms for Isomorphism on Bounded Treewidth Graphs

The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time [Bod90],[YBFT99]. We give restricted space algorithms for these problems proving the following results: - Isomorphism for bounded tree distance width graphs is in L and thus complete for the class. We also show that for this kind of graphs a canon can be computed within logspace. - For bounded treewidth graphs, when both input graphs are given together with a tree decomposition, the problem of whether there is an isomorphism which respects the decompositions (i.e. considering only isomorphisms mapping bags in one decomposition blockwise onto bags in the other decomposition) is in L. - For bounded treewidth graphs, when one of the input graphs is given with a tree decomposition the isomorphism problem is in LogCFL. - As a corollary the isomorphism problem for bounded treewidth graphs is in LogCFL. This improves the known TC1 upper bound for the problem given by Grohe and Verbitsky [GroVer06].Comment: STACS conference 2010, 12 page

Turing machines with few accepting computations and low sets for PP

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The power of the middle bit of a #P function

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Monitoring of SARS-CoV-2 seroprevalence among primary healthcare patients in the Barcelona Metropolitan Area: the SeroCAP sentinel network protocol

Introduction SARS-CoV-2 seroprevalence studies are currently being recommended and implemented in many countries. Forming part of the COVID-19 monitoring and evaluation plan of the Catalan Government Health Department, our network aims to initiate a primary healthcare sentinel monitoring system as a surrogate of SARS-CoV-2 exposure in the Barcelona Metropolitan Area. Methods and analysis The seroCAP is a serial cross-sectional study, which will be performed in the Barcelona Metropolitan Area to estimate antibodies against SARS-CoV-2. From February 2021 to March 2022, the detection of serum IgG antibodies against SARS-CoV-2 trimeric spike protein will be performed on a monthly basis in blood samples collected for diverse clinical purposes in three reference hospitals from the three Barcelona healthcare areas (BCN areas). The samples (n=2588/month) will be from patients attended by 30 primary healthcare teams at 30 basic healthcare areas (BHA). A lab software algorithm will systematically select the samples by age and sex. Seroprevalence will be estimated and monitored by age, sex, BCN area and BHA. Descriptive and cluster analysis of the characteristics and distribution of SARS-CoV-2 infections will be performed. Sociodemographic, socioeconomic and morbidity-associated factors will be determined using logistic regression. We will explore the association between seroprevalence, SARS-CoV-2 confirmed cases and the implemented measures using interrupted time series analysis. Ethics and dissemination Ethical approval was obtained from the University Institute Foundation for Primary Health Care Research Jordi Gol i Gurina ethics committee. An informed consent is not required regarding the approval of the secondary use of biological samples within the framework of the COVID-19 pandemic. A report will be generated quarterly. The final analysis, conclusions and recommendations will be shared with the stakeholders and communicated to the general public. Manuscripts resulting from the network will be submitted for publication in peer-reviewed journals

Reversible Pebble Games and the Relation between Tree-like and General Resolution

We show a new connection between the space measure in tree-like resolution and the reversible pebble game in graphs. Using this connection we provide several formula classes for which there is a logarithmic factor separation between the space complexity measure in tree-like and general resolution. We show that these separations are almost optimal by proving upper bounds for tree-like resolution space in terms of general resolution clause and variable space. In particular we show that for any formula $F$, its tree-like resolution is upper bounded by space$(\pi)\big(\hbox{\rm time}(\pi)\big)$ where $\pi$ is any general resolution refutation of $F$. This holds considering as space$(\pi)$ the clause space of the refutation as well as considering its variable space. For the concrete case of Tseitin formulas we are able to improve this bound to the optimal bound space$(\pi)\log n$, where $n$ is the number of vertices of the corresponding graph.Non UBCUnreviewedAuthor affiliation: University of UlmFacult

CNF and DNF succinct graph encodings

It is well-known that succinct encodings of computational problems – using circuits or formulas to encode large instances – generally result in an exponential complexity blow-up compared to their original complexity. We introduce a new way to encode graph problems, based on CNF or DNF formulas. We show that – contrary to the other existing succinct models – there are examples of problems whose complexity does not increase when encoded in the new form, or increases to an intermediate complexity class less powerful than the exponential blow up. We also study the complexity of the succinct versions of the Graph Isomorphism problem. We show that all the versions are hard for PSPACE. Although the exact complexity of these problems is still unknown, we show that under most existing succinct models the different versions of the problem are equivalent. We also give an algorithm for the DNF encoded version of GI whose running time depends mainly on the number of terms in the succinct representation.by Bireswar Das, Patrick Scharpfenecker and Jacobo Torán