13,177 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
KMS states on Quantum Grammars
We consider quantum (unitary) continuous time evolution of spins on a lattice
together with quantum evolution of the lattice itself. In physics such
evolution was discussed in connection with quantum gravity. It is also related
to what is called quantum circuits, one of the incarnations of a quantum
computer. We consider simpler models for which one can obtain exact
mathematical results. We prove existence of the dynamics in both Schroedinger
and Heisenberg pictures, construct KMS states on appropriate C*-algebras. We
show (for high temperatures) that for each system where the lattice undergoes
quantum evolution, there is a natural scaling leading to a quantum spin system
on a fixed lattice, defined by a renormalized Hamiltonian.Comment: 22 page
Complexity of Problems of Commutative Grammars
We consider commutative regular and context-free grammars, or, in other
words, Parikh images of regular and context-free languages. By using linear
algebra and a branching analog of the classic Euler theorem, we show that,
under an assumption that the terminal alphabet is fixed, the membership problem
for regular grammars (given v in binary and a regular commutative grammar G,
does G generate v?) is P, and that the equivalence problem for context free
grammars (do G_1 and G_2 generate the same language?) is in
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