This contribution shows how to express mathematical abstract notion of <i>n</i>-ary relation by means of Boolean equations. The main criterion of the relation examined in the paper is quantitative criterion, where elements of the domain sets of the relation can be compared just like ordinal numbers, that is can be greater than, equal to or greater or equal to.
The paper concerns the problem of automatic solving of transition conflicts in hierarchical concurrent state machines (also known as UML state machine). Preparing by the designer a formal specification of a behaviour free from conflicts can be very complex. In this paper, it is proposed a method for solving conflicts through transition predicates modification. Partially specified predicates in the nondeterministic diagram are transformed into a symbolic Boolean space, whose points of the space code all possible valuations of transition predicates. Next, all valuations under partial specifications are logically multiplied by a function which represents all possible orthogonal predicate valuations. The result of this operation contains all possible collections of predicates, which under given partial specification make that the original diagram is conflict free and deterministic.
Statechart diagram and UML technique can be a vital part of early conceptual modeling. At the present time there is no much support in hardware design methodologies for reconfiguration features of reprogrammable devices. Authors try to bridge the gap between imprecise UML model and formal HDL description. The key concept in author's proposal is to describe the behavior of the digital controller by statechart diagrams and to map some parts of the behavior into reprogrammable logic by means of group of states which forms sequential automaton. The whole process is illustrated by the example with experimental results.