18,323 research outputs found
Algebraic properties of structured context-free languages: old approaches and novel developments
The historical research line on the algebraic properties of structured CF
languages initiated by McNaughton's Parenthesis Languages has recently
attracted much renewed interest with the Balanced Languages, the Visibly
Pushdown Automata languages (VPDA), the Synchronized Languages, and the
Height-deterministic ones. Such families preserve to a varying degree the basic
algebraic properties of Regular languages: boolean closure, closure under
reversal, under concatenation, and Kleene star. We prove that the VPDA family
is strictly contained within the Floyd Grammars (FG) family historically known
as operator precedence. Languages over the same precedence matrix are known to
be closed under boolean operations, and are recognized by a machine whose pop
or push operations on the stack are purely determined by terminal letters. We
characterize VPDA's as the subclass of FG having a peculiarly structured set of
precedence relations, and balanced grammars as a further restricted case. The
non-counting invariance property of FG has a direct implication for VPDA too.Comment: Extended version of paper presented at WORDS2009, Salerno,Italy,
September 200
Shuffle on array languages generated by array grammars
Motivated by the studies done by G. Siromoney et al. (1973) and Alexan-
dru Mateescu et al. (1998) we examine the language theoretic results related to shuf- fle on trajectories by making use of Siromoney array grammars such as (R : R)AG, (R : C F )AG, (C F : R)AG, (C F : C F )AG, (C S : R)AG, (C S : C S)AG and (C F : C S)AG which are more powerful than the Siromoney matrix grammars (1972)
and are used to make digital pictures
Gaming security by obscurity
Shannon sought security against the attacker with unlimited computational
powers: *if an information source conveys some information, then Shannon's
attacker will surely extract that information*. Diffie and Hellman refined
Shannon's attacker model by taking into account the fact that the real
attackers are computationally limited. This idea became one of the greatest new
paradigms in computer science, and led to modern cryptography.
Shannon also sought security against the attacker with unlimited logical and
observational powers, expressed through the maxim that "the enemy knows the
system". This view is still endorsed in cryptography. The popular formulation,
going back to Kerckhoffs, is that "there is no security by obscurity", meaning
that the algorithms cannot be kept obscured from the attacker, and that
security should only rely upon the secret keys. In fact, modern cryptography
goes even further than Shannon or Kerckhoffs in tacitly assuming that *if there
is an algorithm that can break the system, then the attacker will surely find
that algorithm*. The attacker is not viewed as an omnipotent computer any more,
but he is still construed as an omnipotent programmer.
So the Diffie-Hellman step from unlimited to limited computational powers has
not been extended into a step from unlimited to limited logical or programming
powers. Is the assumption that all feasible algorithms will eventually be
discovered and implemented really different from the assumption that everything
that is computable will eventually be computed? The present paper explores some
ways to refine the current models of the attacker, and of the defender, by
taking into account their limited logical and programming powers. If the
adaptive attacker actively queries the system to seek out its vulnerabilities,
can the system gain some security by actively learning attacker's methods, and
adapting to them?Comment: 15 pages, 9 figures, 2 tables; final version appeared in the
Proceedings of New Security Paradigms Workshop 2011 (ACM 2011); typos
correcte
Quantum automata, braid group and link polynomials
The spin--network quantum simulator model, which essentially encodes the
(quantum deformed) SU(2) Racah--Wigner tensor algebra, is particularly suitable
to address problems arising in low dimensional topology and group theory. In
this combinatorial framework we implement families of finite--states and
discrete--time quantum automata capable of accepting the language generated by
the braid group, and whose transition amplitudes are colored Jones polynomials.
The automaton calculation of the polynomial of (the plat closure of) a link L
on 2N strands at any fixed root of unity is shown to be bounded from above by a
linear function of the number of crossings of the link, on the one hand, and
polynomially bounded in terms of the braid index 2N, on the other. The growth
rate of the time complexity function in terms of the integer k appearing in the
root of unity q can be estimated to be (polynomially) bounded by resorting to
the field theoretical background given by the Chern-Simons theory.Comment: Latex, 36 pages, 11 figure
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