1. A nucleic acid-based molecular computing system, comprising: (i) an input nucleic acid strand comprising a first fragment (A) and a second fragment (B); (ii) a first target, incompletely base-paired nucleic acid duplex comprising a first strand and a second strand, wherein the first strand comprises a first fragment (B′) and a second fragment (A′), the second strand comprises a first fragment (B) and a second fragment (C) and the first target duplex comprises a duplex region formed by base-pairing between B and B′ and two single-stranded regions, A′ and C, and wherein A and B of the input strand can bind with A′ and B′ of the first strand of the first target duplex, respectively, under hybridizing conditions to invoke a strand displacement reaction to produce a first output duplex; (iii) a second target, incompletely base-paired nucleic acid duplex comprising a first strand and a second strand, wherein the first strand comprises a first fragment (C′) and a second fragment (B′), the second strand comprises a first fragment (C) and a second fragment (D) and the second target duplex comprises a duplex region formed by base-pairing between C and C′ and two single-stranded regions B′ and D, wherein B and C of the second strand of the first target duplex can bind with B′ and C′ of the first strand of the second target duplex, respectively, under hybridizing conditions to invoke a strand displacement reaction to produce a second output duplex, and wherein the second fragment (B) of the input strand can bind with the single-stranded region B′ of the second target duplex under hybridizing conditions; and (iii) a third target, incompletely base-paired nucleic acid duplex comprising a first strand and a second strand, wherein the first strand comprises a first fragment (D′) and a second fragment (C′), the second strand comprises a first fragment (D) and a second fragment (E) and the third target duplex comprises a duplex region formed by base-pairing between D and D′ and two single-stranded regions C′ and E, wherein C and D of the second strand of the second target duplex can bind with C′ and D′ of the first strand of the third target duplex, respectively, under hybridizing conditions to invoke a strand displacement reaction to produce a third output duplex, and wherein the second fragment (C) of the second strand of the first target duplex can bind with the single-stranded region C′ of the third target duplex under hybridizing conditions, wherein the first fragment (B) of the second strand of the first target duplex comprises a first chemical modification, relative to a natural nucleic acid, that causes binding with the second fragment (B′) of the first strand of the second target duplex to have a decreased hybridization free energy and/or the second fragment (B) of the input strand comprises a second chemical modification, relative to a natural nucleic acid, that causes binding with the second fragment (B′) of the first strand of the second target duplex to have an increased hybridization free energy, such that the first fragment (B) of the second strand of the first target duplex, as compared to the second fragment (B) of the input strand, binds to the second fragment (B′) of the first strand of the second target duplex to form a more stable duplex region; and wherein the first fragment (C) of the second strand of the second target duplex comprises a third chemical modification, relative to a natural nucleic acid, that causes binding with the second fragment (C′) of the first strand of the third target duplex to have a decreased hybridization free energy and/or the second fragment (C) of the second strand of the first target duplex comprises a fourth chemical modification, relative to a natural nucleic acid, that causes binding with the second fragment (C′) of the first strand of the third target duplex to have an increased hybridization free energy, such that the first fragment (C) of the second strand of the second target duplex, as compared to the second fragment (C) of the second strand of the first target duplex, binds to the second fragment (C′) of the first strand of the third target duplex to form a more stable duplex region.