The Genres of the Pentateuch and Their Social Settings

The ability to recognize genres has been central to modern critical study of the Pentateuch since the work of Hermann Gunkel at the turn of the twentieth century. This essay surveys the legal, administrative, and literary genres used in the Pentateuch, offering a sense of its generic complexity. Genres are defined not as the fixed and stable forms used to classify texts, as understood by classic form-critical method, but as idealized cognitive models employed as tools for writing and interpreting texts, an understanding drawn from modern genre theory. Because genres are situated in social contexts, Gunkel saw genre as central to writing a history of Israel’s literature. This essay surveys the limitations of Gunkel’s vision yet identifies a way to reconnect with it and write a more organic literary history, one that may intersect with but also at times challenge the results of source- and redaction-critical methods.

THE GENERAL COMPLEXITY OF THE PROBLEM TO RECOGNIZE HAMILTONIAN PATHS

Generic-case approach to algorithmic problems has been offered by A. Miasnikov, V. Kapovich, P. Schupp, and V. Shpilrain in 2003. This approach studies an algorithm behavior on typical (almost all) inputs and ignores the rest of inputs. In this paper, we study the generic complexity of the problem of recognition of Hamiltonian paths in finite graphs. A path in graph is called Hamiltonian if it passes through all vertices exactly once. We prove that under the conditions P 6= NP and P = BPP for this problem there is no polynomial strongly generic algorithm. A strongly generic algorithm solves a problem not on the whole set of inputs, but on a subset, the sequence of frequencies of which exponentially quickly converges to 1 with increasing size. To prove the theorem, we use the method of generic amplification, which allows to construct generically hard problems from the problems hard in the classical sense. The main component of this method is the cloning technique, which combines the inputs of a problem together into sufficiently large sets of equivalent inputs. Equivalence is understood in the sense that the problem is solved similarly for them.

ON GENERIC COMPLEXITY OF THE ISOMORPHISM PROBLEM FOR FINITE SEMIGROUPS

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, V. Kapovich, P. Schupp, and V. Shpilrain in 2003. This approach studies behavior of an algorithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we study the generic complexity of the isomorphism problem for finite semigroups. In this problem, for any two semigroups of the same order, given by their multiplication tables, it is required to determine whether they are isomorphic. V. Zemlyachenko, N. Korneenko, and R. Tyshkevich in 1982 proved that the graph isomorphism problem polynomially reduces to this problem. The graph isomorphism problem is a well-known algorithmic problem that has been actively studied since the 1970s, and for which polynomial algorithms are still unknown. So from a computational point of view the studied problem is no simpler than the graph isomorphism problem. We present a generic polynomial algorithm for the isomorphism problem of finite semigroups. It is based on the characterization of almost all finite semigroups as 3-nilpotent semigroups of a special form, established by D. Kleitman, B. Rothschild, and J. Spencer, as well as the Bollobas polynomial algorithm, which solves the isomorphism problem for almost all strongly sparse graphs.

On generic complexity of the subset sum problem in monoids and groups of integer matrix of order two

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algo-rithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we prove that the subset sum problems for the monoid of integer positive unimodular matrices of the second order, the special linear group of the second order, and the modular group are generically solvable in polynomial time.