We study the complexity classes P and NP through a semigroup fP (“polynomial-time functions”), consisting of all polynomially balanced polynomial-time computable partial functions. Then P 6= NP iff fP is a non-regular semigroup. The one-way functions considered here are based on worstcase complexity (they are not cryptographic); they are the non-regular elements of fP. We prove various properti...

We study the problem of finding ordinal utility functions to rank the outcomes of a decision when preference independence between the attributes is not present. We propose that the next level of complexity is to assume that preferences over one attribute can switch at most once as another attribute varies from low to high. We refer to this property as ordinal one-switch independence. We present...

This is a Fuchsian equation of order n with singularities at 0, 1,∞. The local exponents read, 1− β1, . . . , 1− βn at z = 0 α1, . . . , αn at z =∞ 0, 1, . . . , n− 2, −1 + ∑n 1 (βi − αi) at z = 1 When the βi are distinct modulo 1 a basis of solutions at z = 0 is given by the functions z1−βi nFn−1 ( α1 − βi + 1, . . . , αn − βi + 1 β1 − βi + 1, ..∨.., βn − βi + 1 ∣∣∣∣ z) (i = 1, . . . , n). Her...

We show that some problems in information security can be solved without using one-way functions. The latter are usually regarded as a central concept of cryptography, but the very existence of one-way functions depends on difficult conjectures in complexity theory, most notably on the notorious “P 6= NP” conjecture. This is why cryptographic primitives that do not employ one-way functions are ...