13 research outputs found
Capacity Bounded Grammars and Petri Nets
A capacity bounded grammar is a grammar whose derivations are restricted by
assigning a bound to the number of every nonterminal symbol in the sentential
forms. In the paper the generative power and closure properties of capacity
bounded grammars and their Petri net controlled counterparts are investigated
On Languages Accepted by P/T Systems Composed of joins
Recently, some studies linked the computational power of abstract computing
systems based on multiset rewriting to models of Petri nets and the computation
power of these nets to their topology. In turn, the computational power of
these abstract computing devices can be understood by just looking at their
topology, that is, information flow.
Here we continue this line of research introducing J languages and proving
that they can be accepted by place/transition systems whose underlying net is
composed only of joins. Moreover, we investigate how J languages relate to
other families of formal languages. In particular, we show that every J
language can be accepted by a log n space-bounded non-deterministic Turing
machine with a one-way read-only input. We also show that every J language has
a semilinear Parikh map and that J languages and context-free languages (CFLs)
are incomparable
Translation from Classical Two-Way Automata to Pebble Two-Way Automata
We study the relation between the standard two-way automata and more powerful
devices, namely, two-way finite automata with an additional "pebble" movable
along the input tape. Similarly as in the case of the classical two-way
machines, it is not known whether there exists a polynomial trade-off, in the
number of states, between the nondeterministic and deterministic pebble two-way
automata. However, we show that these two machine models are not independent:
if there exists a polynomial trade-off for the classical two-way automata, then
there must also exist a polynomial trade-off for the pebble two-way automata.
Thus, we have an upward collapse (or a downward separation) from the classical
two-way automata to more powerful pebble automata, still staying within the
class of regular languages. The same upward collapse holds for complementation
of nondeterministic two-way machines.
These results are obtained by showing that each pebble machine can be, by
using suitable inputs, simulated by a classical two-way automaton with a linear
number of states (and vice versa), despite the existing exponential blow-up
between the classical and pebble two-way machines
The Nondeterministic Waiting Time Algorithm: A Review
We present briefly the Nondeterministic Waiting Time algorithm. Our technique
for the simulation of biochemical reaction networks has the ability to mimic
the Gillespie Algorithm for some networks and solutions to ordinary
differential equations for other networks, depending on the rules of the
system, the kinetic rates and numbers of molecules. We provide a full
description of the algorithm as well as specifics on its implementation. Some
results for two well-known models are reported. We have used the algorithm to
explore Fas-mediated apoptosis models in cancerous and HIV-1 infected T cells