Document Zbl 1522.68378

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Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13505, 171-187 (2022). </div> <div class="abstract">Summary: Given a system of constraints over a set $X$ of variables, projected model counting asks us to count satisfying assignments of the constraint system projected on a subset $\mathcal{P}$ of $X$. A key idea used in modern projected counters is to first compute an <span class="zbmathjax-textit">independent support</span>, say $\mathcal{I} $, that is often a small subset of $\mathcal{P} $, and to then count models projected on $\mathcal{I}$ instead of on $\mathcal{P} $. While this has been effective in scaling performance of counters, the question of whether we can benefit by projecting on variables beyond $\mathcal{P}$ has not been explored. In this paper, we study this question and show that contrary to intuition, it can be beneficial to project on variables even beyond $\mathcal{P} $. In several applications, a good upper bound of the projected model count often suffices. We show that in several such cases, we can identify a set of variables, called <span class="zbmathjax-textit">upper bound support (UBS)</span>, that is not necessarily a subset of $\mathcal{P} $, and yet counting models projected on UBS guarantees an upper bound of the projected model count. Theoretically, a UBS can be exponentially smaller than the smallest independent support. Our experiments show that even otherwise, UBS-based projected counting can be faster than independent support-based projected counting, while yielding bounds of high quality. Based on extensive experiments, we find that UBS-based projected counting can solve many problem instances that are beyond the reach of a state-of-the-art independent support-based projected model counter.<br class="zbmathjax-paragraph">For the entire collection see [<a href="/1511.68011">Zbl 1511.68011</a>].</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7691501">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68R07" title="MSC2020">68R07</a> </td> <td class="space"> Computational aspects of satisfiability </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68Q60" title="MSC2020">68Q60</a> </td> <td class="space"> Specification and verification (program logics, model checking, etc.) </td> </tr></table> </div> <div class="software"> <h3>Software:</h3><a href="/software/47692">UniGen</a>; <a href="/software/41093">GANAK</a>; <a href="/software/47693">BIRD2</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1522.68378" data-ciurl="/ci/07691501" data-biburl="/bibtex/07691501.bib" data-amsurl="/amsrefs/07691501.bib" data-xmlurl="/xml/07691501.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07691501.pdf" title="Zbl 1522.68378 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/978-3-031-19992-9_11" aria-label="DOI for “Projected model counting: beyond independent support”" title="10.1007/978-3-031-19992-9_11">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2110.09171"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Achlioptas, D.; Theodoropoulos, P.; Gaspers, S.; Walsh, T., Probabilistic model counting with short XORs, Theory and Applications of Satisfiability Testing - SAT 2017, 3-19 (2017), Cham: Springer, Cham · <a href="/1496.68253" class="nowrap">Zbl 1496.68253</a> · <a href="https://doi.org/10.1007/978-3-319-66263-3_1" class="nowrap">doi:10.1007/978-3-319-66263-3_1</a></td> </tr><tr> <td>[2]</td> <td class="space">Agrawal, D., Pote, Y., Meel, K.S.: Partition function estimation: a quantitative study. 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