Abstract
Many modern models of informational defence represents by graphs and partial orders (posets). It is very important to resolve such algorithmic problems as searching of elements that satisfies some conditions (or, another words, to resolve recognition problems) in this models. Algebraic geometry is resolving such problems and find elements from algebraic structure that is solution of system of equations. But before searching the effective algorithms of resolving the systems, first better to answer the essential question: can we resolve the system efficiently? In this article we find the condition to poset which can be efficiently resolve every finite system of equations over the partial orders.
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