Propositional calculus

Unsatisfiable core

In mathematical logic, given an unsatisfiable Boolean propositional formula in conjunctive normal form, a subset of clauses whose conjunction is still unsatisfiable is called an unsatisfiable core of the original formula. Many SAT solvers can produce a resolution graph which proves the unsatisfiability of the original problem. This can be analyzed to produce a smaller unsatisfiable core. An unsatisfiable core is called a minimal unsatisfiable core, if every proper subset (allowing removal of any arbitrary clause or clauses) of it is satisfiable. Thus, such a core is a local minimum, though not necessarily a global one. There are several practical methods of computing minimal unsatisfiable cores. A minimum unsatisfiable core contains the smallest number of the original clauses required to still be unsatisfiable. No practical algorithms for computing the minimum core are known. Notice the terminology: whereas the minimal unsatisfiable core was a local problem with an easy solution, the minimum unsatisfiable core is a global problem with no known easy solution. (Wikipedia).

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Source Boston 2010: Embedded System Hacking and My Plot to Take Over The World 4/5

Clip 4/5 Speaker: Paul Asadoorian, PaulDotCom It seems that as Moore's law is proven time and time again, we as a society are seeing more and more embedded systems help us in our daily lives. Embedded or purpose-built systems those that perform a specific function â are contained in the

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Source Boston 2010: Embedded System Hacking and My Plot to Take Over The World 2/5

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Related pages

Maxima and minima | Conjunctive normal form | Mathematical logic | SAT solver | Propositional formula | Boolean satisfiability problem | Maximal and minimal elements