8,473 research outputs found
Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the
state-complexity of representing sub- or superword closures of context-free
grammars (CFGs): (1) We prove a (tight) upper bound of on
the size of nondeterministic finite automata (NFAs) representing the subword
closure of a CFG of size . (2) We present a family of CFGs for which the
minimal deterministic finite automata representing their subword closure
matches the upper-bound of following from (1).
Furthermore, we prove that the inequivalence problem for NFAs representing sub-
or superword-closed languages is only NP-complete as opposed to PSPACE-complete
for general NFAs. Finally, we extend our results into an approximation method
to attack inequivalence problems for CFGs
Automatic acquisition of LFG resources for German - as good as it gets
We present data-driven methods for the acquisition of LFG resources from two German treebanks. We discuss problems specific to semi-free word order languages as well as problems arising fromthe data structures determined
by the design of the different treebanks. We compare two ways of encoding semi-free word order, as done in the two German treebanks, and argue that the design of the TiGer treebank is more adequate for the acquisition of LFG
resources. Furthermore, we describe an architecture for LFG grammar acquisition for German, based on the two German treebanks, and compare our results with a hand-crafted German LFG grammar
Tightening the Complexity of Equivalence Problems for Commutative Grammars
We show that the language equivalence problem for regular and context-free
commutative grammars is coNEXP-complete. In addition, our lower bound
immediately yields further coNEXP-completeness results for equivalence problems
for communication-free Petri nets and reversal-bounded counter automata.
Moreover, we improve both lower and upper bounds for language equivalence for
exponent-sensitive commutative grammars.Comment: 21 page
Probabilistic mathematical formula recognition using a 2D context-free graph grammar
We present a probabilistic framework for the mathematical expression recognition problem. The developed system is flexible in that its grammar can be extended easily thanks to its graph grammar which eliminates the need for specifying rule precedence. It is also optimal in the sense that all possible interpretations of the expressions are expanded without making early commitments or hard decisions. In this paper, we give an overview of the whole system and describe in detail the graph grammar and the parsing process used in the system, along with some preliminary results on character, structure and expression recognition performances
Equilibria, Fixed Points, and Complexity Classes
Many models from a variety of areas involve the computation of an equilibrium
or fixed point of some kind. Examples include Nash equilibria in games; market
equilibria; computing optimal strategies and the values of competitive games
(stochastic and other games); stable configurations of neural networks;
analysing basic stochastic models for evolution like branching processes and
for language like stochastic context-free grammars; and models that incorporate
the basic primitives of probability and recursion like recursive Markov chains.
It is not known whether these problems can be solved in polynomial time. There
are certain common computational principles underlying different types of
equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP.
Representative complete problems for these classes are respectively, pure Nash
equilibria in games where they are guaranteed to exist, (mixed) Nash equilibria
in 2-player normal form games, and (mixed) Nash equilibria in normal form games
with 3 (or more) players. This paper reviews the underlying computational
principles and the corresponding classes
The Grail theorem prover: Type theory for syntax and semantics
As the name suggests, type-logical grammars are a grammar formalism based on
logic and type theory. From the prespective of grammar design, type-logical
grammars develop the syntactic and semantic aspects of linguistic phenomena
hand-in-hand, letting the desired semantics of an expression inform the
syntactic type and vice versa. Prototypical examples of the successful
application of type-logical grammars to the syntax-semantics interface include
coordination, quantifier scope and extraction.This chapter describes the Grail
theorem prover, a series of tools for designing and testing grammars in various
modern type-logical grammars which functions as a tool . All tools described in
this chapter are freely available
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