Schema simulation

Schema simulation --- схемное моделирование.

Let [math]\displaystyle{ \alpha=(G_\alpha, R_\alpha, \Omega_\alpha) }[/math] be a large-block schema.

A scale [math]\displaystyle{ \Delta }[/math] of [math]\displaystyle{ \alpha }[/math] is such a pair [math]\displaystyle{ (\Delta_1, \Delta_2) }[/math] that [math]\displaystyle{ \Delta_1 }[/math] is a partion of [math]\displaystyle{ G_\alpha }[/math] into disjoint fragments and [math]\displaystyle{ \Delta_2 }[/math] is a partion of [math]\displaystyle{ X_\alpha }[/math] into disjoint subsets.

A schema [math]\displaystyle{ \beta }[/math] simulates [math]\displaystyle{ \alpha }[/math] on the scale [math]\displaystyle{ \Delta }[/math], if the following property holds. For any [math]\displaystyle{ I_1\in \Omega_\alpha }[/math] there is [math]\displaystyle{ I_2\in \Omega_\beta }[/math] such that [math]\displaystyle{ I_1 }[/math] and [math]\displaystyle{ I_2 }[/math] are equal on [math]\displaystyle{ \Sigma_\alpha }[/math]; the execution and memory state sequences of [math]\displaystyle{ \alpha }[/math] under [math]\displaystyle{ I_1 }[/math] and [math]\displaystyle{ \beta }[/math] under [math]\displaystyle{ I_2 }[/math], as well as information connections between the statements, are equal in the sense of the above correspondence.

It is clear that the relation of schema simulation is transitive and that there is such a standard schema [math]\displaystyle{ \alpha }[/math] and its scale [math]\displaystyle{ \Delta }[/math] that any [math]\displaystyle{ \beta }[/math] simulating [math]\displaystyle{ \alpha }[/math] on [math]\displaystyle{ \Delta }[/math] is not a standard schema.

There is an algorithm that, for any large-block schema [math]\displaystyle{ \alpha }[/math] and any scale [math]\displaystyle{ \Delta }[/math] of [math]\displaystyle{ \alpha }[/math], constructs a schema [math]\displaystyle{ \beta }[/math] that simulates [math]\displaystyle{ \alpha }[/math] on [math]\displaystyle{ \Delta }[/math]. But the property of precise schema simulation is not partially decidable in the class of large-block schemas.