# boolean satisfiability Published articles for boolean satisfiability. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Optimization Models for Subset Cover DevFeed: [Optimization Models for Subset Cover]() Original publisher: [Read original article]() Published: 2020-10-20T09:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Optimization](), [Code](), [Open Source]() Tags: [article](), [boolean-satisfiability](), [combinatorics](), [integer-programming](), [mathematics](), [optimization](), [programming](), [python](), [smt](), [source](), [subset-cover](), [z3]() ### AI overview This article explores subset covering as a combinatorial optimization problem and compares Integer Linear Programming solvers with Z3, an open-source SMT solver from Microsoft. It defines a generalized formulation for covering all subsets of size l with the fewest subsets of size k. ### Source excerpt In a recent newsletter article I complained about how researchers mislead about the applicability of their work. I gave SAT solvers as an example. People provided interesting examples in response, but what was new to me was the concept of SMT (Satisfiability Modulo Theories), an extension to SAT. SMT seems to have more practical uses than vanilla SAT (see the newsletter for details). I wanted to take some time to explore SMT solvers, and I landed on Z3, an open-source SMT solver from Microsoft. ## Boolean Logic in Polynomials DevFeed: [Boolean Logic in Polynomials]() Original publisher: [Read original article]() Published: 2017-07-24T09:00:38Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [polynomials](), [Math and Logic](), [Optimization]() Tags: [boolean](), [boolean-satisfiability](), [logic](), [machine-learning](), [np-hard](), [optimization](), [polynomials]() ### AI overview This tutorial shows how to represent Boolean logic formulas with polynomials by using multiplication for conjunction and 1 minus a variable for negation. It explains how the construction relates Boolean satisfiability to the hardness of multivariable polynomial root-finding and constrained polynomial optimization. ### Source excerpt Problem: Express a boolean logic formula using polynomials. I.e., if an input variable $ x$ is set to $ 0$, that is interpreted as false, while $ x=1$ is interpreted as true. The output of the polynomial should be 0 or 1 according to whether the formula is true or false as a whole. Solution: You can do this using a single polynomial. Illustrating with an example: the formula is $ \neg[(a \vee b) \wedge (\neg c \vee d)]$ also known as ## An Update on "Coloring Resilient Graphs" DevFeed: [An Update on "Coloring Resilient Graphs"]() Original publisher: [Read original article]() Published: 2014-07-14T10:00:51Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Graphs](), [Resilience](), [Computer science](), [Mathematics]() Tags: [boolean-satisfiability](), [computer-science](), [graphs](), [np-hard](), [research](), [resilience](), [update]() ### AI overview The article updates a preprint on coloring resilient graphs, announcing its acceptance to the Mathematical Foundations of Computer Science 2014 conference and discussing additional resilience results. It contrasts resilient graph coloring with resilient SAT, where sufficiently resilient instances are either vacuous or NP-hard. ### Source excerpt A while back I announced a preprint of a paper on coloring graphs with certain resilience properties. I'm pleased to announce that it's been accepted to the Mathematical Foundations of Computer Science 2014, which is being held in Budapest this year. Since we first published the preprint we've actually proved some additional results about resilience, and so I'll expand some of the details here. I think it makes for a nicer overall picture, and in my opinion it gives a little more justification that resilient coloring is interesting, at least in contrast to other resilience problems. ## A problem that is not (properly) PAC-learnable DevFeed: [A problem that is not (properly) PAC-learnable]() Original publisher: [Read original article]() Published: 2014-04-21T10:00:16Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Learning](), [math](), [Math and Logic]() Tags: [algorithm](), [boolean](), [boolean-satisfiability](), [classes](), [computational-complexity](), [computational-learning-theory](), [learning-theory](), [logical](), [math](), [mathematics](), [misconceptions](), [np](), [np-completeness](), [pac-learning](), [reduction](), [rp]() ### AI overview This technical learning-theory article presents a standard example of a problem that is not learnable under the previously introduced PAC model, then explains how a more expressive hypothesis class changes that result. Its addendum clarifies that 3-term DNF formulas are not shown to be unlearnable under the standard PAC definition, only under the earlier restricted definition. ### Source excerpt In a previous post we introduced a learning model called Probably Approximately Correct (PAC). We saw an example of a concept class that was easy to learn: intervals on the real line (and more generally, if you did the exercise, axis-aligned rectangles in a fixed dimension). One of the primary goals of studying models of learning is to figure out what is learnable and what is not learnable in the various models.