744 research outputs found
The most nonelementary theory (a direct lower bound proof)
We give a direct proof by generic reduction that a decidable rudimentary theory of finite typed sets [Henkin 63, Meyer 74, Statman 79, Mairson 92] requires space exceeding infinitely often an exponentially growing stack of twos. This gives the highest currently known lower bound for a decidable logical theory and affirmatively answers to Problem 10.13 of [Compton & Henson 90]: Is there a `natural' decidable theory with a lower bound of the form , where is not linearly bounded? The highest previously known lower and upper bounds for `natural' decidable theories, like WS1S, S2S, are `just' linearly growing stacks of twos
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
Method for classification of the computational problems on the basis of the multifractal division of the complexity classes
This paper proposes the method of the multifractal division of the computational complexity classes, which is formalized by introducing the special equivalence relations on these classes. Exposing the self-similarity properties of the complexity classes structure, this method allows performing the accurate classification of the problems and demonstrates the capability of adaptation to the new advances in the computational complexity theory
Game Refinement Relations and Metrics
We consider two-player games played over finite state spaces for an infinite
number of rounds. At each state, the players simultaneously choose moves; the
moves determine a successor state. It is often advantageous for players to
choose probability distributions over moves, rather than single moves. Given a
goal, for example, reach a target state, the question of winning is thus a
probabilistic one: what is the maximal probability of winning from a given
state?
On these game structures, two fundamental notions are those of equivalences
and metrics. Given a set of winning conditions, two states are equivalent if
the players can win the same games with the same probability from both states.
Metrics provide a bound on the difference in the probabilities of winning
across states, capturing a quantitative notion of state similarity.
We introduce equivalences and metrics for two-player game structures, and we
show that they characterize the difference in probability of winning games
whose goals are expressed in the quantitative mu-calculus. The quantitative
mu-calculus can express a large set of goals, including reachability, safety,
and omega-regular properties. Thus, we claim that our relations and metrics
provide the canonical extensions to games, of the classical notion of
bisimulation for transition systems. We develop our results both for
equivalences and metrics, which generalize bisimulation, and for asymmetrical
versions, which generalize simulation
Levelable Sets and the Algebraic Structure of Parameterizations
Asking which sets are fixed-parameter tractable for a given parameterization
constitutes much of the current research in parameterized complexity theory.
This approach faces some of the core difficulties in complexity theory. By
focussing instead on the parameterizations that make a given set
fixed-parameter tractable, we circumvent these difficulties. We isolate
parameterizations as independent measures of complexity and study their
underlying algebraic structure. Thus we are able to compare parameterizations,
which establishes a hierarchy of complexity that is much stronger than that
present in typical parameterized algorithms races. Among other results, we find
that no practically fixed-parameter tractable sets have optimal
parameterizations
- …