Relocability for SCMFSA
نویسندگان
چکیده
In this paper j, k will denote natural numbers. Let p be a finite partial state of SCMFSA and let k be a natural number. The functor Relocated(p, k) yields a finite partial state of SCMFSA and is defined as follows: (Def. 1) Relocated(p, k) = Start-At(ICp + k)+· IncAddr(Shift(ProgramPart(p), k), k)+·DataPart(p). We now state a number of propositions: (1) For every finite partial state p of SCMFSA and for every natural number k holds DataPart(Relocated(p, k)) = DataPart(p). (2) For every finite partial state p of SCMFSA and for every natural number k holds ProgramPart(Relocated(p, k)) = IncAddr(Shift(ProgramPart(p), k), k). (3) For every finite partial state p of SCMFSA holds domProgramPart (Relocated(p, k)) = {insloc(j + k) : insloc(j) ∈ domProgramPart(p)}. (4) Let p be a finite partial state of SCMFSA, and let k be a natural number, and let l be an instruction-location of SCMFSA. Then l ∈ dom p if and only if l + k ∈ domRelocated(p, k). (5) For every finite partial state p of SCMFSA and for every natural number k holds ICSCMFSA ∈ domRelocated(p, k).
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