Biomedical subjects

M Margenstern

Publications and source records attributed to M Margenstern.

3 recordsLinked to original sources

PubMed1999

A universal time-varying distributed H-system of degree 2.

A time-varying distributed H system is a splicing system which has the following feature: at different moments one uses different sets of splicing rules. The number of these sets is called the degree of the system. The passing from a set of rules to another one is specified in a cycle. It is a well known fact that any formal language can be generated by a time-varying distributed H-system of degree at least 7. Here we prove that there are universal time-varying distributed H-systems of degree 2. The question of whether or not there are universal time-varying distributed H-systems of degree 1 remains open.

Animals↗

PubMed1999

Nine switch-affine neurons suffice for Turing universality.

In a previous work Pollack showed that a particular type of heterogeneous processor network is Turing universal. Siegelmann and Sontag (1991) showed the universality of homogeneous networks of first-order neurons having piecewise-linear activation functions. Their result was generalized by Kilian and Siegelmann (1996) to include various sigmoidal activation functions. Here we focus on a type of high-order neurons called switch-affine neurons, with piecewise-linear activation functions, and prove that nine such neurons suffice for simulating universal Turing machines.

Journal Article↗

PubMed1998

Finite H-systems with 3 test tubes are not predictable.

Finite H-systems with n test tubes are splicing systems of n test tubes over a common molecular alphabet, sigma, with a filter Fi [symbol: see text] sigma for each test tube. Initially, arbitrary many copies of molecules and enzymes (splicing rules) from a finite set of molecules and enzymes are given to the test tubes that produce new molecules by splicing and filtering. It is known that any formal language can be generated by a finite H-system with 9 test tubes and that the results of finite H-systems with 6 test tubes are unpredictable. Here we present a rather simple proof that the results of finite H-systems with only 3 test tubes are unpredictable and that 4 test tubes suffices to generate any formal language.

Algorithms↗