The primary goal in this thesis is to identify better syntactic constraint or bias, that is language independent but also efficiently exploitable during sentence processing. We focus on a particular syntactic construction called center-embedding, which is well studied in psycholinguistics and noted to cause particular difficulty for comprehension. Since people use language as a tool for communication, one expects such complex constructions to be avoided for communication efficiency. From a computational perspective, center-embedding is closely relevant to a left-corner parsing algorithm, which can capture the degree of center-embedding of a parse tree being constructed. This connection suggests left-corner methods can be a tool to exploit the universal syntactic constraint that people avoid generating center-embedded structures. We explore such utilities of center-embedding as well as left-corner methods extensively through several theoretical and empirical examinations. Our primary task is unsupervised grammar induction. In this task, the input to the algorithm is a collection of sentences, from which the model tries to extract the salient patterns on them as a grammar. This is a particularly hard problem although we expect the universal constraint may help in improving the performance since it can effectively restrict the possible search space for the model. We build the model by extending the left-corner parsing algorithm for efficiently tabulating the search space except those involving center-embedding up to a specific degree. We examine the effectiveness of our approach on many treebanks, and demonstrate that often our constraint leads to better parsing performance. We thus conclude that left-corner methods are particularly useful for syntax-oriented systems, as it can exploit efficiently the inherent universal constraints in languages.