Referential Data Structures

We introduce reference structures -- a basic logical model of a computer memory organization capable to store and utilize information about its addresses. The corresponding labeled modal logics are axiomatized and supplied with the completeness and decidability theorems. A labeled modal formula can be regarded as a description of a certain reference structure; the satisfiability algorithm gives a method of building and optimizing reference structures satisfying a given formula. 1 Introduction The information about memory blocks addresses are built-in into some data structures, which are arranged in order to provide more fast, more direct access to the memory blocks. For example, a structure list of A 1 ; A 2 ; : : : is a set of records each of which contains a proper data A i together with the address p i+1 of the record containing A i+1 : p 1 stores (A 1 ; p 2 ); p 2 stores (A 2 ; p 3 ); : : : : A structure tree is organized as a set of records containing a proper data together wit..