40 research outputs found
Linear Bounded Composition of Tree-Walking Tree Transducers: Linear Size Increase and Complexity
Compositions of tree-walking tree transducers form a hierarchy with respect
to the number of transducers in the composition. As main technical result it is
proved that any such composition can be realized as a linear bounded
composition, which means that the sizes of the intermediate results can be
chosen to be at most linear in the size of the output tree. This has
consequences for the expressiveness and complexity of the translations in the
hierarchy. First, if the computed translation is a function of linear size
increase, i.e., the size of the output tree is at most linear in the size of
the input tree, then it can be realized by just one, deterministic,
tree-walking tree transducer. For compositions of deterministic transducers it
is decidable whether or not the translation is of linear size increase. Second,
every composition of deterministic transducers can be computed in deterministic
linear time on a RAM and in deterministic linear space on a Turing machine,
measured in the sum of the sizes of the input and output tree. Similarly, every
composition of nondeterministic transducers can be computed in simultaneous
polynomial time and linear space on a nondeterministic Turing machine. Their
output tree languages are deterministic context-sensitive, i.e., can be
recognized in deterministic linear space on a Turing machine. The membership
problem for compositions of nondeterministic translations is nondeterministic
polynomial time and deterministic linear space. The membership problem for the
composition of a nondeterministic and a deterministic tree-walking tree
translation (for a nondeterministic IO macro tree translation) is log-space
reducible to a context-free language, whereas the membership problem for the
composition of a deterministic and a nondeterministic tree-walking tree
translation (for a nondeterministic OI macro tree translation) is possibly
NP-complete
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection
Extended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of 2O(n) for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of (1.056 + o(1))n for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case. (c) IFIP International Federation for Information Processing 2016
Efficient Parallel Path Checking for Linear-Time Temporal Logic With Past and Bounds
Path checking, the special case of the model checking problem where the model
under consideration is a single path, plays an important role in monitoring,
testing, and verification. We prove that for linear-time temporal logic (LTL),
path checking can be efficiently parallelized. In addition to the core logic,
we consider the extensions of LTL with bounded-future (BLTL) and past-time
(LTL+Past) operators. Even though both extensions improve the succinctness of
the logic exponentially, path checking remains efficiently parallelizable: Our
algorithm for LTL, LTL+Past, and BLTL+Past is in AC^1(logDCFL) \subseteq NC
On the Complexity of Free Word Orders
International audienceWe propose some extensions of mildly context-sensitive for- malisms whose aim is to model free word orders in natural languages. We give a detailed analysis of the complexity of the formalisms we propose
Computational Complexity and Graph Isomorphism
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic, that is, structurally the same. The complexity of graph isomorphism is an open problem and it is one of the few problems in NP which is neither known to be solvable in polynomial time nor NP-complete. It is one of the most researched open problems in theoretical computer science.
The foundations of computability theory are in recursion theory and in recursive functions which are an older model of computation than Turing machines. In this master’s thesis we discuss the basics of the recursion theory and the main theorems starting from the axioms. The aim of the second chapter is to define the most important T- and m-reductions and the implication hierarchy between reductions.
Different variations of Turing machines include the nondeterministic and oracle Turing machines. They are discussed in the third chapter. A hierarchy of different complexity classes can be created by reducing the available computational resources of recursive functions. The members of this hierarchy include for instance P and NP. There are hundreds of known complexity classes and in this work the most important ones regarding graph isomorphism are introduced.
Boolean circuits are a different method for approaching computability. Some main results and complexity classes of circuit complexity are discussed in the fourth chapter. The aim is to show that graph isomorphism is hard for the class DET.
Graph isomorphism is known to belong to the classes coAM and SPP. These classes are introduced in the fifth chapter by using theory of probabilistic classes, polynomial hierarchy, interactive proof systems and Arthur-Merlin games. Polynomial hierarchy collapses to its second level if GI is NP-complete