42,772 research outputs found
Going higher in the First-order Quantifier Alternation Hierarchy on Words
We investigate the quantifier alternation hierarchy in first-order logic on
finite words. Levels in this hierarchy are defined by counting the number of
quantifier alternations in formulas. We prove that one can decide membership of
a regular language to the levels (boolean combination of
formulas having only 1 alternation) and (formulas having only 2
alternations beginning with an existential block). Our proof works by
considering a deeper problem, called separation, which, once solved for lower
levels, allows us to solve membership for higher levels
Constraint Satisfaction and Semilinear Expansions of Addition over the Rationals and the Reals
A semilinear relation is a finite union of finite intersections of open and
closed half-spaces over, for instance, the reals, the rationals, or the
integers. Semilinear relations have been studied in connection with algebraic
geometry, automata theory, and spatiotemporal reasoning. We consider semilinear
relations over the rationals and the reals. Under this assumption, the
computational complexity of the constraint satisfaction problem (CSP) is known
for all finite sets containing R+={(x,y,z) | x+y=z}, <=, and {1}. These
problems correspond to expansions of the linear programming feasibility
problem. We generalise this result and fully determine the complexity for all
finite sets of semilinear relations containing R+. This is accomplished in part
by introducing an algorithm, based on computing affine hulls, which solves a
new class of semilinear CSPs in polynomial time. We further analyse the
complexity of linear optimisation over the solution set and the existence of
integer solutions.Comment: 22 pages, 1 figur
Computing with cells: membrane systems - some complexity issues.
Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism
Unbounded-error quantum computation with small space bounds
We prove the following facts about the language recognition power of quantum
Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more
powerful than probabilistic Turing machines for any common space bound
satisfying . For "one-way" Turing machines, where the
input tape head is not allowed to move left, the above result holds for
. We also give a characterization for the class of languages
recognized with unbounded error by real-time quantum finite automata (QFAs)
with restricted measurements. It turns out that these automata are equal in
power to their probabilistic counterparts, and this fact does not change when
the QFA model is augmented to allow general measurements and mixed states.
Unlike the case with classical finite automata, when the QFA tape head is
allowed to remain stationary in some steps, more languages become recognizable.
We define and use a QTM model that generalizes the other variants introduced
earlier in the study of quantum space complexity.Comment: A preliminary version of this paper appeared in the Proceedings of
the Fourth International Computer Science Symposium in Russia, pages
356--367, 200
Underapproximation of Procedure Summaries for Integer Programs
We show how to underapproximate the procedure summaries of recursive programs
over the integers using off-the-shelf analyzers for non-recursive programs. The
novelty of our approach is that the non-recursive program we compute may
capture unboundedly many behaviors of the original recursive program for which
stack usage cannot be bounded. Moreover, we identify a class of recursive
programs on which our method terminates and returns the precise summary
relations without underapproximation. Doing so, we generalize a similar result
for non-recursive programs to the recursive case. Finally, we present
experimental results of an implementation of our method applied on a number of
examples.Comment: 35 pages, 3 figures (this report supersedes the STTT version which in
turn supersedes the TACAS'13 version
A Comparison of Relaxations of Multiset Cannonical Correlation Analysis and Applications
Canonical correlation analysis is a statistical technique that is used to
find relations between two sets of variables. An important extension in pattern
analysis is to consider more than two sets of variables. This problem can be
expressed as a quadratically constrained quadratic program (QCQP), commonly
referred to Multi-set Canonical Correlation Analysis (MCCA). This is a
non-convex problem and so greedy algorithms converge to local optima without
any guarantees on global optimality. In this paper, we show that despite being
highly structured, finding the optimal solution is NP-Hard. This motivates our
relaxation of the QCQP to a semidefinite program (SDP). The SDP is convex, can
be solved reasonably efficiently and comes with both absolute and
output-sensitive approximation quality. In addition to theoretical guarantees,
we do an extensive comparison of the QCQP method and the SDP relaxation on a
variety of synthetic and real world data. Finally, we present two useful
extensions: we incorporate kernel methods and computing multiple sets of
canonical vectors
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
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