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We consider the original Lambek calculus and its natural modification called the Lambek calculus allowing empty premises. Both calculi have three binary connectives: an associative product operator and its two residuals, the left and right division. This paper contains a short survey of complexity results concerning fragments of these calculi obtained by restricting the set of connectives and/or the number of variables. ======================================================== URL: http://www.mathnet.ru/php/presentation.phtml?presentid=483