TY - GEN

T1 - On the computational power of neural nets

AU - Siegelmann, Hava T.

AU - Sontag, Eduardo D.

PY - 1992

Y1 - 1992

N2 - This paper deals with finite networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a `sigmoidal' scalar nonlinearity to a linear combination of the previous states of all units. We prove that one may simulate all Turing Machines by rational nets. In particular, one can do this in linear time, and there is a net made up of about 1,000 processors which computes a universal partial-recursive function. Products (high order nets) are not required, contrary to what had been stated in the literature. Furthermore, we assert a similar theorem about non-deterministic Turing Machines. Consequences for undecidability and complexity issues about nets are discussed too.

AB - This paper deals with finite networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a `sigmoidal' scalar nonlinearity to a linear combination of the previous states of all units. We prove that one may simulate all Turing Machines by rational nets. In particular, one can do this in linear time, and there is a net made up of about 1,000 processors which computes a universal partial-recursive function. Products (high order nets) are not required, contrary to what had been stated in the literature. Furthermore, we assert a similar theorem about non-deterministic Turing Machines. Consequences for undecidability and complexity issues about nets are discussed too.

UR - http://www.scopus.com/inward/record.url?scp=0026972451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026972451&partnerID=8YFLogxK

U2 - 10.1145/130385.130432

DO - 10.1145/130385.130432

M3 - Conference contribution

AN - SCOPUS:0026972451

SN - 089791497X

SN - 9780897914970

T3 - Proceedings of the Fifth Annual ACM Workshop on Computational Learning Theory

SP - 440

EP - 449

BT - Proceedings of the Fifth Annual ACM Workshop on Computational Learning Theory

PB - Publ by ACM

T2 - Proceedings of the Fifth Annual ACM Workshop on Computational Learning Theory

Y2 - 27 July 1992 through 29 July 1992

ER -