Most modal logics such as S5, LTL, or ATL are extensions of Modal Logic K. While the model checking problems for LTL and to a lesser extent ATL have been very active research areas for the past decades, the model checking problem for the more basic Multi-agent Modal Logic K (MMLK) has important applications as a formal framework for perfect information multi-player games on its own. We present Minimal Proof Search (MPS), an effort number based algorithm solving the model checking problem for MMLK. We prove two important properties for MPS beyond its correctness. The (dis)proof exhibited by MPS is of minimal cost for a general definition of cost, and MPS is an optimal algorithm for finding (dis)proofs of minimal cost. Optimality means that any comparable algorithm either needs to explore a bigger or equal state space than MPS, or is not guaranteed to find a (dis)proof of minimal cost on every input. As such, our work relates to A* and AO* in heuristic search, to Proof Number Search and DFPN+ in two-player games, and to counterexample minimization in software model checking.

Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover, a number of recent applications motivated various extensions of this problem. For example, unsatisfiable formulas partitioned into disjoint subsets of clauses (so-called groups) often need to be simplified by removing redundant groups, or may contain redundant variables, rather than clauses. In this report we present a generalized theoretical framework of labelled CNF formulas that unifies various extensions of the redundancy detection and removal problem and allows to derive a number of results that subsume and extend previous work. The follow-up reports contain a number of additional theoretical results and algorithms for various computational problems in the context of the proposed framework.

This manuscript contains the proofs for "A Primal-Dual Message-Passing Algorithm for Approximated Large Scale Structured Prediction" We derive the Lagrangian by introducing the Lagrange multipliers Anymaa (33") for every marginalization constraint:13an bggfiyfiafija): bawdy"), and Lagrange multipliers 0r for every equality We obtain the dual function by minimizing the beliefs over their compact domain, i.e. Deriving the dual by minimizing over the compact set of beliefs enables us to obtain an unconstrained dual, which corresponds to the approximated structured prediction program. Its final form is derived similarly to Claim. We find the optimal Amyyywoxgv) whenever the gradient vanishes, i.e. A Hx7y7afiv (3912) 'i' Anymaa (go) $957971?

We address the issue of edge detection in Synthetic Aperture Radar imagery. In particular, we propose nonparametric methods for edge detection, and numerically compare them to an alternative method that has been recently proposed in the literature. Our results show that some of the proposed methods display superior results and are computationally simpler than the existing method. An application to real (not simulated) data is presented and discussed.

This paper is motivated by the practical problem of how to meaningfully perform sparse regression when the predictor variables are observed with measurement error or some source of uncertainty. We will refer to this error or noise as design uncertainty to emphasize that perturbations in the design matrix may arise from a number of random sources unrelated to experimental or measurement error per se. Recent workin this areahasjust begun to addressthe issue ofsparseregressionunder design uncertainty from a theoretical point of view. We are primarily interested in describing an approach that, while theoretically justifiable, is essentially pragmatic and broadly applicable. In short, we argue that greed - a basic feature of many sparsity promoting algorithms - is indeed good [Tropp, 2004], so long as the design data is scaled by the uncertainty variances. We demonstrate the efficacy of scaling from several points of view and validate it empirically with a biomass characterization data set using two of the most widely used sparse algorithms: least angle regression (LARS) and the Dantzig selector (DS). Our work was motivated by an example from a biomass characterization experiment related to work at the National Renewable Energy Laboratory. The example is described in detail in Section 4 and contains repeated measurements of mass spectral (design, or predictor) and sugar mass fraction (response) values within each switchgrass sample. The domain scientists' goal was to find a small subset of masses in the spectrum that could be used to predict sugar mass fraction.

Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to have an exact solution. In this case one may use heuristic approach to obtain a near-optimal solution in some reasonable time. We focus on two combinatorial optimization problems, namely the Generalized Traveling Salesman Problem and the Multidimensional Assignment Problem. The first problem is an important generalization of the Traveling Salesman Problem; the second one is a generalization of the Assignment Problem for an arbitrary number of dimensions. Both problems are NP-hard and have hosts of applications. In this work, we discuss different aspects of heuristics design and evaluation. A broad spectrum of related subjects, covered in this research, includes test bed generation and analysis, implementation and performance issues, local search neighborhoods and efficient exploration algorithms, metaheuristics design and population sizing in memetic algorithm. The most important results are obtained in the areas of local search and memetic algorithms for the considered problems. In both cases we have significantly advanced the existing knowledge on the local search neighborhoods and algorithms by systematizing and improving the previous results. We have proposed a number of efficient heuristics which dominate the existing algorithms in a wide range of time/quality requirements. Several new approaches, introduced in our memetic algorithms, make them the state-of-the-art metaheuristics for the corresponding problems. Population sizing is one of the most promising among these approaches; it is expected to be applicable to virtually any memetic algorithm.

We revisit the SeqBin constraint. This meta-constraint subsumes a number of important global constraints like Change, Smooth and IncreasingNValue. We show that the previously proposed filtering algorithm for SeqBin has two drawbacks even under strong restrictions: it does not detect bounds disentailment and it is not idempotent. We identify the cause for these problems, and propose a new propagator that overcomes both issues. Our algorithm is based on a connection to the problem of finding a path of a given cost in a restricted $n$-partite graph. Our propagator enforces domain consistency in O(nd^2) and, for special cases of SeqBin that include Change, Smooth and IncreasingNValue, in O(nd) time.

We propose a probabilistic formulation that enables sequential detection of multiple change points in a network setting. We present a class of sequential detection rules for certain functionals of change points (minimum among a subset), and prove their asymptotic optimality properties in terms of expected detection delay time. Drawing from graphical model formalism, the sequential detection rules can be implemented by a computationally efficient message-passing protocol which may scale up linearly in network size and in waiting time. The effectiveness of our inference algorithm is demonstrated by simulations.

The multiple attribute mixed type decision making is performed by four methods, that is, the relative approach degree of grey TOPSIS method, the relative approach degree of grey incidence, the relative membership degree of grey incidence and the grey relation relative approach degree method using the maximum entropy estimation, respectively. In these decision making methods, the grey incidence degree in four-dimensional Euclidean space is used. The final arrangement result is obtained by weighted Borda method. An example illustrates the applicability of the proposed approach.

Hidden Markov Models (HMMs) (Baum and Eagon, 1967; Rabiner, 1989) are the workhorse statistical model for discrete time series, with widely diverse applications including automatic speech recognition, natural language processing (NLP), and genomic sequence modeling. In this model, a discrete hidden state evolves according to some Markovian dynamics, and observations at a particular time depend only on the hidden state at that time. The learning problem is to estimate the model only with observation samples from the underlying distribution. Thus far, the predominant learning algorithms have been local search heuristics, such as the Baum-Welch / EM algorithm (Baum et al., 1970; Dempster et al., 1977). It is not surprising that practical algorithms have resorted to heuristics, as the general learning problem has been shown to be hard under cryptographic assumptions (Terwijn, 2002). Fortunately, the hardness results are for HMMs that seem divorced from those that we are likely to encounter in practical applications. The situation is in many ways analogous to learning mixture distributions with samples from the underlying distribution. There, the general problem is also believed to be hard. However, much recent progress has been made when certain separation assumptions are made with respect to the component mixture distributions (e.g.