degree 1 curves in the dwork pencil and the mirror quintic we give a description of the relative hilbert scheme of lines in the dwork pencil of quintic threefolds we describe the corresponding relative hilbert scheme associated to the mirror family of quintic threefolds

quantum finite automata we first outline main steps and achievements along bertoni s research path in quantum finite automata theory from the very basic definitions of the models of quantum finite automata throughout the investigation of their computational and descriptional power next we choose to focus on bertoni s studies on quantum finite automata descriptional complexity in particular we expand on a statistical framework for the synthesis of succinct quantum finite automata discussing its adaptation to the case of multiperiodic events and languages we then improve such a framework to obtain even more succinct quantum finite automata for some multiperiodic languages finally we introduce some promise problems for multiperiodic inputs showing that even on this class of problems the descriptional power of quantum finite automata greatly outperforms that of equivalent classical finite automata we build small size monte carlo quantum finite automata for multiperiodic languages we analyze the modular architecture of such monte carlo quantum finite automata we solve promise problems on multiperiodic inputs by small quantum finite automata

quantum automata and quantum grammars abstract to study quantum computation it might be helpful to generalize structures from language and automata theory to the quantum case to that end we propose quantum versions of finite state and push down automata and regular and context free grammars we find analogs of several classical theorems including pumping lemmas closure properties rational and algebraic generating functions and greibach normal form we also show that there are quantum context free languages that are not context free so qcfl cfl

de finetti s coherence and statistical inference on donne la definition d une inference coherente en conformite avec une theorie des probabilites conditionnelles derivee du principe de coherence de de finetti et on effectue une comparaison critique d une telle definition avec celle proposee par heath lane et sudderth

regular languages accepted by quantum automata in this paper we analyze some features of the behaviour of quantum automata in particular we prove that the class of languages recognized by quantum automata with isolated cut point is the class of reversible regular languages as a more general result we give a bound on the inverse error that implies the regularity of the language accepted by a quantum automaton

sure wins separating probabilities and the representation of linear functionals abstract we discuss conditions under which a convex cone k r admits a finitely additive probability m such that sup k k m k 0 based on these we characterise those linear functionals that are representable as finitely additive expectations a version of riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions

lines on the fermat quintic threefold and the infinitesimal generalized hodge conjecture we study the deformation theory of lines on the fermat quintic threefold we formulate an infinitesimal version of the generalized hodge conjecture and use our analysis of lines to prove it in a special case

strengths and weaknesses of quantum computing recently a great deal of attention has been focused on quantum computation following a sequence of results bernstein and vazirani in proc 25th annual acm symposium theory comput 1993 pp 11 20 siam j comput 26 1997 pp 1277 1339 simon in proc 35th annual ieee symposium foundations comput sci 1994 pp 116 123 siam j comput 26 1997 pp 1340 1349 shor in proc 35th annual ieee symposium foundations comput sci 1994 pp 124 134 suggesting that quantum computers are more powerful than classical probabilistic computers following shor s result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time it is natural to ask whether all of np can be efficiently solved in quantum polynomial time in this paper we address this question by proving that relative to an oracle chosen uniformly at random with probability 1 the class np cannot be solved on a quantum turing machine qtm in time o 2 n 2 we also show that relative to a permutation oracle chosen uniformly at random with probability 1 the class np cap conp cannot be solved on a qtm in time o 2 n 3 the former bound is tight since recent work of grover in it proc 28 th annual acm symposium theory comput 1996 shows how to accept the class np relative to any oracle on a quantum computer in time o 2 n 2

small size quantum automata recognizing some regular languages given a class p i of stochastic events induced by m state 1 way quantum finite automata 1qfa on alphabet we investigate the size number of states of 1qfa s that approximate a convex linear combination of p i and we apply the results to the synthesis of small size 1qfa s we obtain an o md 3 log2 d 2 general size bound where d is the vapnik dimension of p w w for commutative n periodic events p on with h we prove an o h log n 2 size bound for inducing a approximation of p whenever f p 1 nh where f p is the discrete fourier transform of the vector p associated with p if the characteristic function l of an n periodic unary language l satisfies f l 1 n then l is recognized with isolated cut point by a 1qfa with o log n states vice versa if l is recognized with isolated cut point by a 1qfa with o log n state then f l 1 o n log n

lines on the dwork quintic pencil and its higher degree analogues we give a reformulation of the recent results of candelas et al lines on the dwork pencil of quintic threefolds describing pencils of lines on the quintic threefold x 1 dots x 5 in mathbb p 4 mathbb c vert x 5 1 dots x 5 5 5 psi x 1 dots x 5 in terms of the moduli space m 0 5 of curves of genus 0 with 5 marked points and a generalization to pencils of lines on the degree n hypersurfaces x 1 dots x n in mathbb p n 1 mathbb c vert x n 1 dots x n n n psi x 1 dots x n in mathbb p n 1 mathbb c in terms of the moduli space m 0 n for any odd integer n geq 5

quantum mechanical hamiltonian models of turing machines quantum mechanical hamiltonian models which represent an aribtrary but finite number of steps of any turing machine computation are constructed here on a finite lattice of spin 1 2 systems different regions of the lattice correspond to different components of the turing machine plus recording system successive states of any machine computation are represented in the model by spin configuration states both time independent and time dependent hamiltonian models are constructed here the time independent models do not dissipate energy or degrade the system state as they evolve they operate close to the quantum limit in that the total system energy uncertainty computation speed is close to the limit given by the time energy uncertainty relation however the model evolution is time global and the hamiltonian is more complex the time dependent models do not degrade the system state also they are time local and the hamiltonian is less complex

state complexity of operations on two way finite automata over a unary alphabet the paper determines the number of states in two way deterministic finite automata 2dfa over a one letter alphabet sufficient and in the worst case necessary to represent the results of basic language theoretic operations on 2dfas with a certain number of states it is proved that i intersection of an m state 2dfa and an n state 2dfa requires between m n and m n 1 states ii union of an m state 2dfa and an n state 2dfa between m n and 2m n 4 states iii kleene star of an n state 2dfa g n o n 2 states where g n e 1 o 1 n l n n is the maximum value of lcm p 1 p k for p i

improved constructions of quantum automata we present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata our automata use email protected states to recognize a language that requires p states classically the construction is both substantially simpler and achieves a better constant in the front of logp than the previously known construction our construction is by a probabilistic argument we consider the possibility to derandomize it and present some results in this direction

geometry of formal kuranishi theory abstract the principle ambient cohomology of a kaehler manifold annihilates obstructions has been known and exploited since pioneering work of kodaira this paper unifies and modestly extends known results in the context of abstract deformations of compact kaehler manifolds and submanifolds

quantum automata for some multiperiodic languages we exhibit small size measure once one way quantum finite automata mo 1qfa s inducing multiperiodic stochastic events moreover for certain classes of multiperiodic languages we exhibit i isolated cut point mo 1qfa s whose size logarithmically depends on the periods ii monte carlo mo 1qfa s whose size logarithmically depends on the periods and polynomially on the inverse of the error probability

the theorem of halmos and savage under finite additivity abstract we prove an extension to the finitely additive setting of the theorem of halmos and savage from this we deduce extensions of classical results of drewnowski and of yan as well as a new characterization of weak compactness in the space of finitely additive set functions

finite automata and unary languages abstract we prove that o e n log n states are sufficient to simulate an n state 1nfa recognizing a unary language by a 1dfa the lower bound is the same similar tight bounds are shown for the simulation of a 2dfa by a 1dfa and a 1nfa we also show that o n 2 states are sufficient and necessary to simulate an n state 1nfa recognizing a unary language by a 2dfa

analogies and differences between quantum and stochastic automata abstract we analyze some features of the behaviour of quantum automata providing analogies and differences with the corresponding stochastic models in particular we prove there is a quantum automaton where the change of state depends on unitary transformations defined by matrices with nonnull amplitudes that accepts a non regular language with cut point zero and inverse error polynomially bounded stochastic automata with matrices having nonnull elements and with polynomial bounds on the inverse error recognize only regular languages the class of stochastic languages contains the class of quantum languages quantum languages are empty or contain an infinite number of words the class of quantum languages is not closed under complementation

decidable and undecidable problems about quantum automata we study the following decision problem is the language recognized by a quantum finite automaton empty or nonempty we prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or nonstrict thresholds this result is in contrast with the corresponding situation for probabilistic finite automata for which it is known that strict and nonstrict thresholds both lead to undecidable problems

size lower bounds for quantum automata we analyze the descriptional power of quantum finite automata with control language we show an exponential size cost conversion from qfas with control language to dfas we simulate latvian qfas by qfas with control languages we obtain size lower bounds for several models of qfas we compare the descriptional power of quantum finite automata with control language qfcs and deterministic finite automata dfas by suitably adapting rabin s technique we show how to convert any given qfc to an equivalent dfa incurring in an at most exponential size increase this enables us to state a lower bound on the size of qfcs which is logarithmic in the size of equivalent minimal dfas in turn this result yields analogous size lower bounds for several models of quantum finite automata in the literature

the complexity of promise problems with applications to public key cryptography a promise problem is a formulation of partial decision problem complexity issues about promise problems arise from considerations about cracking problems for public key cryptosystems using a notion of turing reducibility between promise problems this paper disproves a conjecture made by even and yacobi 1980 that would imply nonexistence of public key cryptosystems with np hard cracking problems in its place a new conjecture is raised having the same consequence in addition the new conjecture implies that np complete sets cannot be accepted by turing machines that have at most one accepting computation for each input word

two way finite automata with quantum and classical states we introduce 2 way finite automata with quantum and classical states 2qcfa s this is a variant on the 2 way quantum finite automata 2qfa model which may be simpler to implement than unrestricted 2qfa s the internal state of a 2qcfa may include a quantum part that may be in a mixed quantum state but the tape head position is required to be classical we show two languages for which 2qcfa s are better than classical 2 way automata first 2qcfa s can recognize palindromes a language that cannot be recognized by 2 way deterministic or probabilistic finite automata second in polynomial time 2qcfa s can recognize anbn n n a language that can be recognized classically by a 2 way probabilistic automaton but only in exponential time

rapid solution of problems by quantum computation a class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method the quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation

membership problems for regular and context free trace languages abstract trace languages have been introduced in order to describe the behaviour of concurrent systems in the same way as usual formal languages do for sequential system they can be defined as subsets of a free partially commutative monoid and a theory of trace languages can be developed generalizing the usual formal languages theory in this paper the time complexity of membership problems for regular and context free trace languages is investigated it is proved that the membership problem for context free trace languages can be solved in time o bm n where is the dimension of the greatest clique of the concurrency relation c and bm n is the time required for multiplying two arbitrary n n boolean matrices for regular trace languages our method gives an algorithm which requires o n time finally the uniform membership problem is shown to be np complete

quantum theory the church turing principle and the universal quantum computer it is argued that underlying the church turing hypothesis there is an implicit physical assertion here this assertion is presented explicitly as a physical principle every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means classical physics and the universal turing machine because the former is continuous and the latter discrete do not obey the principle at least in the strong form above a class of model computing machines that is the quantum generalization of the class of turing machines is described and it is shown that quantum theory and the universal quantum computer are compatible with the principle computing machines resembling the universal quantum computer could in principle be built and would have many remarkable properties not reproducible by any turing machine these do not include the computation of non recursive functions but they do include quantum parallelism a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it the intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than everett s some of the numerous connections between the quantum theory of computation and the rest of physics are explored quantum complexity theory allows a physically more reasonable definition of the complexity or knowledge in a physical system than does classical complexity theory