359 research outputs found
Turing machines based on unsharp quantum logic
In this paper, we consider Turing machines based on unsharp quantum logic.
For a lattice-ordered quantum multiple-valued (MV) algebra E, we introduce
E-valued non-deterministic Turing machines (ENTMs) and E-valued deterministic
Turing machines (EDTMs). We discuss different E-valued recursively enumerable
languages from width-first and depth-first recognition. We find that
width-first recognition is equal to or less than depth-first recognition in
general. The equivalence requires an underlying E value lattice to degenerate
into an MV algebra. We also study variants of ENTMs. ENTMs with a classical
initial state and ENTMs with a classical final state have the same power as
ENTMs with quantum initial and final states. In particular, the latter can be
simulated by ENTMs with classical transitions under a certain condition. Using
these findings, we prove that ENTMs are not equivalent to EDTMs and that ENTMs
are more powerful than EDTMs. This is a notable difference from the classical
Turing machines.Comment: In Proceedings QPL 2011, arXiv:1210.029
Healthiness from Duality
Healthiness is a good old question in program logics that dates back to
Dijkstra. It asks for an intrinsic characterization of those predicate
transformers which arise as the (backward) interpretation of a certain class of
programs. There are several results known for healthiness conditions: for
deterministic programs, nondeterministic ones, probabilistic ones, etc.
Building upon our previous works on so-called state-and-effect triangles, we
contribute a unified categorical framework for investigating healthiness
conditions. We find the framework to be centered around a dual adjunction
induced by a dualizing object, together with our notion of relative
Eilenberg-Moore algebra playing fundamental roles too. The latter notion seems
interesting in its own right in the context of monads, Lawvere theories and
enriched categories.Comment: 13 pages, Extended version with appendices of a paper accepted to
LICS 201
Weighted automata and multi-valued logics over arbitrary bounded lattices
AbstractWe show that L-weighted automata, L-rational series, and L-valued monadic second order logic have the same expressive power, for any bounded lattice L and for finite and infinite words. We also prove that aperiodicity, star-freeness, and L-valued first-order and LTL-definability coincide. This extends classical results of Kleene, Büchi–Elgot–Trakhtenbrot, and others to arbitrary bounded lattices, without any distributivity assumption that is fundamental in the theory of weighted automata over semirings. In fact, we obtain these results for large classes of strong bimonoids which properly contain all bounded lattices
Quantum Finite Automata and Logic
Elektroniskā versija nesatur pielikumusAnotācija
Atslēgas vārdi – kvantu automāti, loģika, automāti bezgalīgiem vārdiem.
Matemātiskās loģikas un klasiskās skaitļošanas saistībai ir bijusi liela nozīme datorzinātnes attīstībā.
Tas ir galvenais iemesls, kas raisījis interesi pētīt kvantu skaitļošanas un loģikas saistību.
Promocijas darbs aplūko saistību starp galīgiem kvantu automātiem un loģiku. Pamatā pētījumi
balstās uz galīgu kvantu automātu un tā dažādiem veidiem (galīgu kvantu automātu ar mērījumu
beigās, galīgu kvantu automātu ar mērījumu katrā solī, galīgo "latviešu" kvantu automātu),
precīzāk, valodām, ko akceptē dažādie kvantu automātu modeļi, un to saistību ar valodām, ko
apraksta dažādie loģikas veidi ( pirmās kārtas loģika, modulārā loģika u.c.). Darbā ir arī aplūkoti
galīgi kvantu automāti, kas akceptē bezgalīgus vārdus.Abstract
Keywords – quantum automata, logic, automata over infinite words
The connection between the classical computation and mathematical logic has had a great impact in
the computer science which is the main reason for the interest in the connection between the
quantum computation and mathematical logic. The thesis studies a connection between quantum
finite state automata and logic. The main research area is a quantum finite state automaton and its
different notations (measure-once quantum finite automaton, measure-many quantum finite
automaton, and Latvian quantum finite automaton), more precisely, the languages accepted by the
various models of the quantum finite state automaton and its connection to languages described by
the different kinds of logic. Additionally, a quantum finite state automaton over infinite words is
introduced
- …