Watchlist (also hint list) is a mechanism that allows related proofs to guide a proof search for a new conjecture. This mechanism has been used with the Otter and Prover9 theorem provers, both for interactive formalizations and for human-assisted proving of open conjectures in small theories. In this work we explore the use of watchlists in large theories coming from first-order translations of large ITP libraries, aiming at improving hammer-style automation by smarter internal guidance of the ATP systems. In particular, we (i) design watchlist-based clause evaluation heuristics inside the E ATP system, and (ii) develop new proof guiding algorithms that load many previous proofs inside the ATP and focus the proof search using a dynamically updated notion of proof matching. The methods are evaluated on a large set of problems coming from the Mizar library, showing significant improvement of E's standard portfolio of strategies, and also of the previous best set of strategies invented for Mizar by evolutionary methods.
: Instead of the strict notion of subsumption, more abstract or heuristic matching methods could be used. An interesting symbolic method to consider is matching modulo symbol alignments @cite_3 . A number of approximate methods are already used by the above mentioned statistical guiding methods.
@cite_3
2345969517 2747550417 2010392031 2435338979
Abstract Alignment-free approaches are gaining persistent interest in many sequence analysis applications such as phylogenetic inference and metagenomic classification clustering, especially for large-scale sequence datasets. Besides the widely used k-mer methods, the average common substring (ACS) approach has emerged to be one of the well-known alignment-free approaches. Two recent works further generalize this ACS approach by allowing a bounded number k of mismatches in the common substrings, relying on approximation (linear time) and exact computation, respectively. Albeit having a good worst-case time complexity aastex amsbsy amsfonts amssymb bm mathrsfs pifont stmaryrd textcomp portland, xspace amsmath, amsxtra empty 10 9 7 6 @math log ^ ... Estimating dense visual correspondences between objects with intra-class variation, deformations and background clutter remains a challenging problem. Thanks to the breakthrough of CNNs there are new powerful features available. Despite their easy accessibility and great success, existing semantic flow methods could not significantly benefit from these without extensive additional training. We introduce a novel method for semantic matching with pre-trained CNN features which is based on convolutional feature pyramids and activation guided feature selection. For the final matching we propose a sparse graph matching framework where each salient feature selects among a small subset of nearest neighbors in the target image. To improve our method in the unconstrained setting without bounding box annotations we introduce novel object proposal based matching constraints. Furthermore, we show that the sparse matching can be transformed into a dense correspondence field. Extensive experimental evaluations on benchmark datasets show that our method significantly outperforms existing semantic matching methods. Approximate matching of strings is reviewed with the aim of surveying techniques suitable for finding an item in a database when there may be a spelling mistake or other error in the keyword. The methods found are classified as either equivalence or similarity problems. Equivalence problems are seen to be readily solved using canonical forms. For sinuiarity problems difference measures are surveyed, with a full description of the wellestablmhed dynamic programming method relating this to the approach using probabilities and likelihoods. Searches for approximate matches in large sets using a difference function are seen to be an open problem still, though several promising ideas have been suggested. Approximate matching (error correction) during parsing is briefly reviewed. In numerous domains it is useful to represent a single example by the set of the local features or parts that comprise it. However, this representation poses a challenge to many conventional machine learning techniques, since sets may vary in cardinality and elements lack a meaningful ordering. Kernel methods can learn complex functions, but a kernel over unordered set inputs must somehow solve for correspondences---generally a computationally expensive task that becomes impractical for large set sizes. We present a new fast kernel function called the pyramid match that measures partial match similarity in time linear in the number of features. The pyramid match maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in order to find implicit correspondences based on the finest resolution histogram cell where a matched pair first appears. We show the pyramid match yields a Mercer kernel, and we prove bounds on its error relative to the optimal partial matching cost. We demonstrate our algorithm on both classification and regression tasks, including object recognition, 3-D human pose inference, and time of publication estimation for documents, and we show that the proposed method is accurate and significantly more efficient than current approaches.