1,734 research outputs found
An Alternative Conception of Tree-Adjoining Derivation
The precise formulation of derivation for tree-adjoining grammars has
important ramifications for a wide variety of uses of the formalism, from
syntactic analysis to semantic interpretation and statistical language
modeling. We argue that the definition of tree-adjoining derivation must be
reformulated in order to manifest the proper linguistic dependencies in
derivations. The particular proposal is both precisely characterizable through
a definition of TAG derivations as equivalence classes of ordered derivation
trees, and computationally operational, by virtue of a compilation to linear
indexed grammars together with an efficient algorithm for recognition and
parsing according to the compiled grammar.Comment: 33 page
Markov chains, -trivial monoids and representation theory
We develop a general theory of Markov chains realizable as random walks on
-trivial monoids. It provides explicit and simple formulas for the
eigenvalues of the transition matrix, for multiplicities of the eigenvalues via
M\"obius inversion along a lattice, a condition for diagonalizability of the
transition matrix and some techniques for bounding the mixing time. In
addition, we discuss several examples, such as Toom-Tsetlin models, an exchange
walk for finite Coxeter groups, as well as examples previously studied by the
authors, such as nonabelian sandpile models and the promotion Markov chain on
posets. Many of these examples can be viewed as random walks on quotients of
free tree monoids, a new class of monoids whose combinatorics we develop.Comment: Dedicated to Stuart Margolis on the occasion of his sixtieth
birthday; 71 pages; final version to appear in IJA
The Complexity of Graph-Based Reductions for Reachability in Markov Decision Processes
We study the never-worse relation (NWR) for Markov decision processes with an
infinite-horizon reachability objective. A state q is never worse than a state
p if the maximal probability of reaching the target set of states from p is at
most the same value from q, regard- less of the probabilities labelling the
transitions. Extremal-probability states, end components, and essential states
are all special cases of the equivalence relation induced by the NWR. Using the
NWR, states in the same equivalence class can be collapsed. Then, actions
leading to sub- optimal states can be removed. We show the natural decision
problem associated to computing the NWR is coNP-complete. Finally, we ex- tend
a previously known incomplete polynomial-time iterative algorithm to
under-approximate the NWR
A Symbolic Intruder Model for Hash-Collision Attacks
In the recent years, several practical methods have been published to compute
collisions on some commonly used hash functions. In this paper we present a
method to take into account, at the symbolic level, that an intruder actively
attacking a protocol execution may use these collision algorithms in reasonable
time during the attack. Our decision procedure relies on the reduction of
constraint solving for an intruder exploiting the collision properties of hush
functions to constraint solving for an intruder operating on words
Inferring Different Types of Lindenmayer Systems Using Artificial Intelligence
Lindenmayer systems (L-systems) are a formal grammar system which consist of a set of rewriting rules. Each rewriting rule is comprised of a symbol to replace (predecessor), a replacement string (successor), and an optional condition that is necessary for replacement. Starting with an initial string, every symbol in the string is replaced in parallel in accordance with the conditions on the rewriting rules, to produce a new string. The replacement process iterates as needed to produce a sequence of strings. There are different types of L-systems, which allow for different types of conditions, and methods of selecting the rules to apply. Some symbols of the alphabet can be interpreted as instructions for simulation software towards process modelling, where each string describes another step of the simulated process.
Typically, creating an L-system for a specific process is done by experts by making meticulous measurements and using a priori knowledge about the process. It would be desirable to have a method to automatically learn the L-systems (the simulation program) from data, such as from a temporal sequence of images. This thesis presents a suite of tools, collectively called the Plant Model Inference Tools or PMIT (despite the name, the tools are domain agnostic), for inferring different types of L-systems using only a sequence of strings describing the process over some initial time period. Variants of PMIT are created for deterministic context-free L-systems, stochastic L-systems, and parametric L-systems. They are each evaluated using existing known deterministic and parametric L-systems from the literature, and procedurally generated stochastic L-systems. Accuracy can be detected in various ways, such as checking whether the inferred L-system is equal to the original one. PMIT is able to correctly infer deterministic L-systems with up to 31 symbols in the alphabet compared to the previous state-of-the-art algorithm's limit of 2 symbols. Stochastic L-systems allow symbols in the alphabet to have multiple rewriting rules each with an associated probability of being selected. Evaluating stochastic L-system inference with 960 procedurally generated L-systems with multiple sequences of strings as input found the following: 1) when 3 input sequences are used, the inferred successors always matched the original successors for systems with up to 9 rewriting rules, 2) when 6 sequences of strings are used, the difference between the associated probabilities of the inferred and the original L-system is approximately 1%. Parametric L-systems allow symbols to have multiple rewriting rules with parameters that get passed during rewriting. Rule selection is based on an associated Boolean condition over the parameters that gets evaluated to choose the rule to be applied. Inference is done in two steps. In the first step, the successors are inferred, and in the second step, appropriate Boolean conditions are found. Parametric L-system inference was evaluated on 20 known parametric L-systems. For 18 of the 20 L-systems where all successors were non-empty, the successors were correctly identified, but the time taken was up to 26 days on a single core CPU for the largest L-system. The second step, inferring the Boolean conditions, was successful for all 20 systems in the test set. No previous algorithm from the literature had implemented stochastic or parametric L-system inference.
Inferring L-systems of greater complexity algorithmically can save considerable time and effort versus constructing them manually; however, perhaps more importantly rather than relying on existing knowledge, inferring a simulation of a process from data can help reveal the underlying scientific principles of the process
Answering Queries using Views over Probabilistic XML: Complexity and Tractability
We study the complexity of query answering using views in a probabilistic XML
setting, identifying large classes of XPath queries -- with child and
descendant navigation and predicates -- for which there are efficient (PTime)
algorithms. We consider this problem under the two possible semantics for XML
query results: with persistent node identifiers and in their absence.
Accordingly, we consider rewritings that can exploit a single view, by means of
compensation, and rewritings that can use multiple views, by means of
intersection. Since in a probabilistic setting queries return answers with
probabilities, the problem of rewriting goes beyond the classic one of
retrieving XML answers from views. For both semantics of XML queries, we show
that, even when XML answers can be retrieved from views, their probabilities
may not be computable. For rewritings that use only compensation, we describe a
PTime decision procedure, based on easily verifiable criteria that distinguish
between the feasible cases -- when probabilistic XML results are computable --
and the unfeasible ones. For rewritings that can use multiple views, with
compensation and intersection, we identify the most permissive conditions that
make probabilistic rewriting feasible, and we describe an algorithm that is
sound in general, and becomes complete under fairly permissive restrictions,
running in PTime modulo worst-case exponential time equivalence tests. This is
the best we can hope for since intersection makes query equivalence intractable
already over deterministic data. Our algorithm runs in PTime whenever
deterministic rewritings can be found in PTime.Comment: VLDB201
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