0-1 Laws for Recursive Structures

More About Recursive Structures: Descriptive Complexity and Zero-One Laws

This paper continues our work on innnite, recursive structures. We investigate the descriptive complexity of several logics over recursive structures, including rst-order, second-order, and xpoint logic, exhibiting connections between expressibility of a property and its computational complexity. We then address 0{1 laws, proposing a version that applies to recursive structures, and using it to...

Monadic Second Order Probabilities in Algebra

We analyze the question of existence of asymptotic cumulative probabilities for monadic second order deenable properties of nite algebras. We focus our attention on the directly representable varieties and on the variety of groups. We prove in a very strong way that some recently proven rst-order 0{1 laws and limit laws for these varieties cannot be extended to monadic second order logic. Namel...

Limit laws for random recursive structures and algorithms

Towards a Theory of Recursive Structures

In computer science, one is interested mainly in nite objects. Insofar as innnite objects are of interest, they must be computable, i.e., recursive, thus admitting an eeective nite representation. This leads to the notion of a recursive graph, or, more generally, a recursive structure , model or data base. In this paper we summarize our recent work on recursive structures and data bases, includ...

A General Limit Theorem for Recursive Algorithms and Combinatorial Structures

Limit laws are proven by the contraction method for random vectors of a recursive nature as they arise as parameters of combinatorial structures such as random trees or recursive algorithms, where we use the Zolotarev metric. In comparison to previous applications of this method, a general transfer theorem is derived which allows us to establish a limit law on the basis of the recursive structu...