TL;DR: It was found that theclass of context-sensitive languages is learnable from an informant, but that not even the class of regular languages is learningable from a text.
Abstract: Language learnability has been investigated. This refers to the following situation: A class of possible languages is specified, together with a method of presenting information to the learner about an unknown language, which is to be chosen from the class. The question is now asked, “Is the information sufficient to determine which of the possible languages is the unknown language?” Many definitions of learnability are possible, but only the following is considered here: Time is quantized and has a finite starting time. At each time the learner receives a unit of information and is to make a guess as to the identity of the unknown language on the basis of the information received so far. This process continues forever. The class of languages will be considered learnable with respect to the specified method of information presentation if there is an algorithm that the learner can use to make his guesses, the algorithm having the following property: Given any language of the class, there is some finite time after which the guesses will all be the same and they will be correct. In this preliminary investigation, a language is taken to be a set of strings on some finite alphabet. The alphabet is the same for all languages of the class. Several variations of each of the following two basic methods of information presentation are investigated: A text for a language generates the strings of the language in any order such that every string of the language occurs at least once. An informant for a language tells whether a string is in the language, and chooses the strings in some order such that every string occurs at least once. It was found that the class of context-sensitive languages is learnable from an informant, but that not even the class of regular languages is learnable from a text.
TL;DR: This approach allows an efficient and natural way to construct iconic indexes for pictures and proves the necessary and sufficient conditions to characterize ambiguous pictures for reduced 2D strings as well as normal 2-D strings.
Abstract: In this paper, we describe a new way of representing a symbolic picture by a two-dimensional string. A picture query can also be specified as a 2-D string. The problem of pictorial information retrieval then becomes a problem of 2-D subsequence matching. We present algorithms for encoding a symbolic picture into its 2-D string representation, reconstructing a picture from its 2-D string representation, and matching a 2-D string with another 2-D string. We also prove the necessary and sufficient conditions to characterize ambiguous pictures for reduced 2-D strings as well as normal 2-D strings. This approach thus allows an efficient and natural way to construct iconic indexes for pictures.
TL;DR: In this article, the role of the homotopy associative A ∞ algebra, the odd symplectic structure, cyclicity, star conjugation, and twist was clarified, and the possible tensor constructions of open string theories were analyzed from first principles.
TL;DR: In this paper, a method and apparatus for automated test input generation for web applications is described, which comprises performing a source-to-source transformation of the program, performing interpretation on the program based on a set of test input values; symbolically executing the program; recording a symbolic constraint for each of one or more conditional expressions encountered during execution, including analyzing a string operation in the program to identify possible execution paths, and generating symbolic inputs representing values of variables in each of the conditional expressions as a numeric expression and a string constraint including generating constraints on string values.
Abstract: A method and apparatus is disclosed herein for automated test input generation for web applications. In one embodiment, the method comprises performing a source-to-source transformation of the program; performing interpretation on the program based on a set of test input values; symbolically executing the program; recording a symbolic constraint for each of one or more conditional expressions encountered during execution of the program, including analyzing a string operation in the program to identify one or more possible execution paths, and generating symbolic inputs representing values of variables in each of the conditional expressions as a numeric expression and a string constraint including generating constraints on string values by modeling string operations using finite state transducers (FSTs) and supplying values from the program's execution in place of intractable sub-expressions; and generating new inputs to drive the program during a subsequent iteration based on results of solving the recorded string constraints.