Geodesic
Structures computable in polynomial time.~I
Algebra i logika, Tome 55 (2016) no. 6, pp. 647-669.

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It is proved that every computable locally finite structure with finitely many functions has a presentation computable in polynomial time. Furthermore, a structure computable in polynomial time is polynomially categorical iff it is finite. If a structure is computable in polynomial time and locally finite then it is weakly polynomially categorical (i.e., categorical with respect to primitive recursive isomorphisms) iff it is finite.
Keywords: locally finite structure, computable structure, structure computable in polynomial time, polynomially categorical structure, weakly polynomially categorical structure. 
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P. E. Alaev. Structures computable in polynomial time.~I. Algebra i logika, Tome 55 (2016) no. 6, pp. 647-669. http://geodesic.mathdoc.fr/item/AL_2016_55_6_a0/

[1] D. Cenzer, J. B. Remmel, “Complexity theoretic model theory and algebra”, Handbook of recursive mathematics, v. 1, Stud. Logic Found. Math., 138, Recursive model theory, eds. Yu. L. Ershov et al., Elsevier, Amsterdam, 1998, 381–513 | DOI | MR | Zbl

[2] D. Cenzer, J. Remmel, “Polynomial-time versus recursive models”, Ann. Pure Appl. Logic, 54:1 (1991), 17–58 | DOI | MR | Zbl

[3] S. Grigorieff, “Every recursive linear ordering has a copy in DTIME-SPACE $(n,\log(n))$”, J. Symb. Log., 55:1 (1990), 260–276 | DOI | MR | Zbl

[4] D. Cenzer, J. Remmel, “Polynomial-time abelian groups”, Ann. Pure Appl. Logic, 56:1–3 (1992), 313–363 | DOI | MR | Zbl

[5] E. I. Latkin, “Polinomialnaya neavtoustoichivost. Algebraicheskii podkhod”, Logicheskie metody v programmirovanii, Sb., Vychisl. sist., 133, In-t matem. SO AN SSSR, Novosibirsk, 1990, 14–37 | MR

[6] E. I. Latkin, “Abstraktnyi funktsional, ogranichivayuschii algoritmicheskuyu slozhnost dlya lineinogo, polinomialnogo i drugikh skhozhikh klassov”, Strukturnye i slozhnostnye problemy vychislimosti, Sb., Vychislit. sist., 165, In-t matem. im. S. L. Soboleva SO RAN, Novosibirsk, 1999, 84–111 | MR

[7] I. Kalimullin, A. Melnikov, K. M. Ng, “Algebraic structures computable without delay”, Theoret. Comput. Sci. (to appear)

[8] P. E. Alaev, “Suschestvovanie i edinstvennost struktur, vychislimykh za polinomialnoe vremya”, Algebra i logika, 55:1 (2016), 106–112 | Zbl

[9] A. Akho, Dzh. Khopkroft, Dzh. Ulman, Postroenie i analiz vychislitelnykh algoritmov, Mir, M., 1979

[10] D. Cenzer, J. B. Remmel, “Complexity and categoricity”, Inf. Comput., 140:1 (1998), 2–25 | DOI | MR | Zbl