Modular verification of DNA strand displacement networks via serializability analysis (APPENDICES)
نویسندگان
چکیده
Proof (of Lemma 2). Assume that S `C t t0. By definition we get that S `C t. If (CANCEL) was used to derive S `C t t0 then t has the form t1 :t2 :t3 and t0 has the form t1 :t3, and furthermore we know that S t1 ! S0 t2 ! S0. It follows immediately that S `C t1:t3, and hence that S `C t0 and finalC(S, t) = finalC(S, t 0), as required. On the other hand, if (SWAP) was used to derive S `C t t0 then t has the form t1:t2:t3:t4 and t0 has the form t1:t3:t2:t4. Furthermore, we know that S `C t1:t3:t2, and finalC(S, t1:t3:t2) = finalC(S, t1:t2:t3). Thus it follows that S `C t1:t3:t2:t4, and hence that S `C t0 and finalC(S, t) = finalC(S, t 0), as required. The cases for the remaining rules, (REFL) and (TRANS), are straightforward. u t
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Modular Verification of DNA Strand Displacement Networks via Serializability Analysis
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