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Volumn 59, Issue 5, 1996, Pages 251-254

A size-depth trade-off for the analog computation of Boolean functions

Author keywords

Arithmetic threshold circuits; Boolean functions; Computational complexity; Size depth trade offs

Indexed keywords


EID: 0043041154     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-0190(96)00120-2     Document Type: Article
Times cited : (1)

References (23)
  • 1
    • 84968516134 scopus 로고
    • On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines
    • L. Blum, M. Shub and S. Smale, On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines, Bull. Amer. Math. Soc. 21 (1989) 1-46.
    • (1989) Bull. Amer. Math. Soc. , vol.21 , pp. 1-46
    • Blum, L.1    Shub, M.2    Smale, S.3
  • 4
    • 38249009165 scopus 로고
    • Two P-complete problems in the theory of reals
    • F. Cucker and A. Torrecillas, Two P-complete problems in the theory of reals, J. Complexity 8 (1992) 454-466.
    • (1992) J. Complexity , vol.8 , pp. 454-466
    • Cucker, F.1    Torrecillas, A.2
  • 5
    • 0041575063 scopus 로고
    • The depth of boolean functions
    • in Russian
    • S.B. Gashkov, The depth of Boolean functions, Prob. Kibernetiki 34 (1978) 265-268 (in Russian).
    • (1978) Prob. Kibernetiki , vol.34 , pp. 265-268
    • Gashkov, S.B.1
  • 6
    • 0043078047 scopus 로고
    • The complexity of the realization of boolean functions by networks of functional elements and by formulas in bases whose elements realize continuous functions
    • in Russian
    • S.B. Gashkov, The complexity of the realization of Boolean functions by networks of functional elements and by formulas in bases whose elements realize continuous functions, Prob. Kibernetiki 37 (1980) 52-118 (in Russian).
    • (1980) Prob. Kibernetiki , vol.37 , pp. 52-118
    • Gashkov, S.B.1
  • 7
    • 0029256399 scopus 로고
    • Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers
    • P. Goldberg and M. Jerrum, Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers, Machine Learning 18 (1995) 131-148.
    • (1995) Machine Learning , vol.18 , pp. 131-148
    • Goldberg, P.1    Jerrum, M.2
  • 9
    • 0042577299 scopus 로고
    • Tech. Rept. NC-TR-94-5, NeuroCOLT Technical Reports Series, August
    • P. Koiran, A weak version of the Blum, Shub & Smale model, Tech. Rept. NC-TR-94-5, NeuroCOLT Technical Reports Series, August 1994; A preliminary version appeared in: Proc. 34th IEEE Symp. on the Foundations of Computer Science (1993) 486-495.
    • (1994) A Weak Version of the Blum, Shub & Smale Model
    • Koiran, P.1
  • 10
    • 0347636199 scopus 로고
    • A preliminary version appeared
    • P. Koiran, A weak version of the Blum, Shub & Smale model, Tech. Rept. NC-TR-94-5, NeuroCOLT Technical Reports Series, August 1994; A preliminary version appeared in: Proc. 34th IEEE Symp. on the Foundations of Computer Science (1993) 486-495.
    • (1993) Proc. 34th IEEE Symp. on the Foundations of Computer Science , pp. 486-495
  • 11
    • 0042076259 scopus 로고
    • A comparison of the computational power of sigmoid and boolean threshold circuits
    • V. Roychowdhury, K.-Y. Siu and A. Orlitsky, eds., Kluwer, Dordrecht
    • W. Maass, G. Schnitger and E.D. Sontag, A comparison of the computational power of sigmoid and Boolean threshold circuits, in: V. Roychowdhury, K.-Y. Siu and A. Orlitsky, eds., Theoretical Advances in Neural Computation and Learning (Kluwer, Dordrecht, 1994) 127-151; A preliminary version appeared in: Proc. 32nd IEEE Symp. on the Foundations of Computer Science (1991) 767-776.
    • (1994) Theoretical Advances in Neural Computation and Learning , pp. 127-151
    • Maass, W.1    Schnitger, G.2    Sontag, E.D.3
  • 12
    • 0043078049 scopus 로고
    • A preliminary version appeared
    • W. Maass, G. Schnitger and E.D. Sontag, A comparison of the computational power of sigmoid and Boolean threshold circuits, in: V. Roychowdhury, K.-Y. Siu and A. Orlitsky, eds., Theoretical Advances in Neural Computation and Learning (Kluwer, Dordrecht, 1994) 127-151; A preliminary version appeared in: Proc. 32nd IEEE Symp. on the Foundations of Computer Science (1991) 767-776.
    • (1991) Proc. 32nd IEEE Symp. on the Foundations of Computer Science , pp. 767-776
  • 13
    • 84966260816 scopus 로고
    • On the Betti numbers of real varieties
    • J. Milnor, On the Betti numbers of real varieties, Proc. Amer. Math. Soc. 15 (1964) 275-280.
    • (1964) Proc. Amer. Math. Soc. , vol.15 , pp. 275-280
    • Milnor, J.1
  • 15
    • 0038384211 scopus 로고
    • Approximating threshold circuits by rational functions
    • R. Paturi and M. Saks, Approximating threshold circuits by rational functions, Inform. and Comput. 112 (1994) 257-272.
    • (1994) Inform. and Comput. , vol.112 , pp. 257-272
    • Paturi, R.1    Saks, M.2
  • 17
    • 0028385008 scopus 로고
    • Rational approximation techniques for analysis of neural networks
    • K.Y. Siu, V.P. Roychowdhury and T. Kailath, Rational approximation techniques for analysis of neural networks, IEEE Trans. Inform. Theory 40 (2) (1994) 455-466.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , Issue.2 , pp. 455-466
    • Siu, K.Y.1    Roychowdhury, V.P.2    Kailath, T.3
  • 18
    • 0041575077 scopus 로고
    • On the computation of boolean functions by analog circuits of bounded fan-in
    • Gy. Turán and F. Vatan, On the computation of Boolean functions by analog circuits of bounded fan-in, in: Proc. 35th IEEE Symp. on the Foundations of Computer Science (1994) 553-564; complete version in: J. Comput. System Sci., to appear.
    • (1994) Proc. 35th IEEE Symp. on the Foundations of Computer Science , pp. 553-564
    • Turán, Gy.1    Vatan, F.2
  • 19
    • 0041575078 scopus 로고    scopus 로고
    • complete version, to appear
    • Gy. Turán and F. Vatan, On the computation of Boolean functions by analog circuits of bounded fan-in, in: Proc. 35th IEEE Symp. on the Foundations of Computer Science (1994) 553-564; complete version in: J. Comput. System Sci., to appear.
    • J. Comput. System Sci.
  • 20
    • 84968495010 scopus 로고
    • Lower bounds for approximation by non-linear manifolds
    • H.E. Warren, Lower bounds for approximation by non-linear manifolds, Trans. Amer. Math. Soc. 133 (1968) 167-178.
    • (1968) Trans. Amer. Math. Soc. , vol.133 , pp. 167-178
    • Warren, H.E.1
  • 23
    • 0020160026 scopus 로고
    • On parallel computation for the knapsack problem
    • A.C. Yao, On parallel computation for the knapsack problem, J. ACM 29 (1982) 898-903.
    • (1982) J. ACM , vol.29 , pp. 898-903
    • Yao, A.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.