255 research outputs found
The Complexity of the Exponential Output Size Problem for Top-Down and Bottom-Up Tree Transducers,
AbstractThe exponential output size problem is to determine whether the size of output trees of a tree transducer grows exponentially in the size of input trees. In this paper the complexity of this problem is studied. It is shown to be NL-complete for total top-down tree transducers, DEXPTIME-complete for general top-down tree transducers, and P-complete for bottom-up tree transducers
MAT learners for recognizable tree languages and tree series
We review a family of closely related query learning algorithms for unweighted and weighted tree automata, all of which are based on adaptations of the minimal adequate teacher (MAT) model by Angluin. Rather than presenting
new results, the goal is to discuss these algorithms in sufficient detail to make their similarities and differences transparent to the reader interested in grammatical inference of tree automata
Analyzing Catastrophic Backtracking Behavior in Practical Regular Expression Matching
We develop a formal perspective on how regular expression matching works in
Java, a popular representative of the category of regex-directed matching
engines. In particular, we define an automata model which captures all the
aspects needed to study such matching engines in a formal way. Based on this,
we propose two types of static analysis, which take a regular expression and
tell whether there exists a family of strings which makes Java-style matching
run in exponential time.Comment: In Proceedings AFL 2014, arXiv:1405.527
Optimal Strategies for Static Black-Peg AB Game With Two and Three Pegs
The AB~Game is a game similar to the popular game Mastermind. We study a
version of this game called Static Black-Peg AB~Game. It is played by two
players, the codemaker and the codebreaker. The codemaker creates a so-called
secret by placing a color from a set of colors on each of pegs,
subject to the condition that every color is used at most once. The codebreaker
tries to determine the secret by asking questions, where all questions are
given at once and each question is a possible secret. As an answer the
codemaker reveals the number of correctly placed colors for each of the
questions. After that, the codebreaker only has one more try to determine the
secret and thus to win the game.
For given and , our goal is to find the smallest number of
questions the codebreaker needs to win, regardless of the secret, and the
corresponding list of questions, called a -strategy. We present a
-strategy for for all , and a -strategy for for all and show the optimality
of both strategies, i.e., we prove that no -strategy for a smaller
exists
Context-free tree grammars are as powerful as context-free jungle grammars
Jungles generalize trees by sharing subtrees and allowing garbage. It is shown that IO context-free tree grammars generate the same jungle languages as context-free jungle grammars. Also, they define the same subsets of any algebra
Generating Semantic Graph Corpora with Graph Expansion Grammar
We introduce Lovelace, a tool for creating corpora of semantic graphs. The
system uses graph expansion grammar as a representational language, thus
allowing users to craft a grammar that describes a corpus with desired
properties. When given such grammar as input, the system generates a set of
output graphs that are well-formed according to the grammar, i.e., a graph
bank. The generation process can be controlled via a number of configurable
parameters that allow the user to, for example, specify a range of desired
output graph sizes. Central use cases are the creation of synthetic data to
augment existing corpora, and as a pedagogical tool for teaching formal
language theory.Comment: In Proceedings NCMA 2023, arXiv:2309.0733
Resource-Bound Quantification for Graph Transformation
Graph transformation has been used to model concurrent systems in software
engineering, as well as in biochemistry and life sciences. The application of a
transformation rule can be characterised algebraically as construction of a
double-pushout (DPO) diagram in the category of graphs. We show how
intuitionistic linear logic can be extended with resource-bound quantification,
allowing for an implicit handling of the DPO conditions, and how resource logic
can be used to reason about graph transformation systems
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