We consider the problems of finding the lexicographically minimal (or maximal) satisfying assignment of propositional formulae for different restricted formula classes. It turns out that for each class from our framework, the above problem is either polynomial time solvable or complete for OptP . We also consider the problem of deciding if in the optimal assignment the largest variable gets val...

We introduce partial lexicographic preference trees (PLPtrees) as a formalism for compact representations of preferences over combinatorial domains. Our main results concern the problem of passive learning of PLP-trees. Specifically, for several classes of PLP-trees, we study how to learn (i) a PLPtree consistent with a dataset of examples, possibly subject to requirements on the size of the tr...

In this paper, the two-stage procedure is considered for autoregressive parameters estimation in the p-order autoregressive model ( AR(p)). The point estimation and fixed-size confidence ellipsoids construction are investigated which are based on least-squares estimators. Performance criteria are shown including asymptotically risk efficient, asymptotically efficient, and asymptotically consist...

We consider innnitary logic with two variable symbols and counting quantiiers, C 2 , and its intersection with Ptime on nite relational structures. In particular we exhibit a Ptime canonization procedure for nite relational structures which provides unique representatives up to equivalence in C 2. As a consequence we obtain a recursive presentation for the class of all those queries on arbitrar...

SAT is not in P is proved, in a first-order theory, with a new single finite axiom of Turing’s theory of computing. So, P is not equal to NP.