17 research outputs found
VLDL Satisfiability and Model Checking via Tree Automata
We present novel algorithms solving the satisfiability problem and the model
checking problem for Visibly Linear Dynamic Logic (VLDL) in asymptotically
optimal time via a reduction to the emptiness problem for tree automata with
B\"uchi acceptance. Since VLDL allows for the specification of important
properties of recursive systems, this reduction enables the efficient analysis
of such systems.
Furthermore, as the problem of tree automata emptiness is well-studied, this
reduction enables leveraging the mature algorithms and tools for that problem
in order to solve the satisfiability problem and the model checking problem for
VLDL.Comment: 14 page
Simulation Over One-counter Nets is PSPACE-Complete
One-counter nets (OCN) are Petri nets with exactly one unbounded place. They
are equivalent to a subclass of one-counter automata with just a weak test for
zero. Unlike many other semantic equivalences, strong and weak simulation
preorder are decidable for OCN, but the computational complexity was an open
problem. We show that both strong and weak simulation preorder on OCN are
PSPACE-complete.Comment: Extended version of material presented at the FST&TCS 2013
conference. 22 page
Computing the Width of Non-deterministic Automata
International audienceWe introduce a measure called width, quantifying the amount of nondetermin-ism in automata. Width generalises the notion of good-for-games (GFG) automata, that correspond to NFAs of width 1, and where an accepting run can be built on-the-fly on any accepted input. We describe an incremental determinisation construction on NFAs, which can be more efficient than the full powerset determinisation, depending on the width of the input NFA. This construction can be generalised to infinite words, and is particularly well-suited to coBüchi automata. For coBüchi automata, this procedure can be used to compute either a deterministic automaton or a GFG one, and it is algorithmically more efficient in the last case. We show this fact by proving that checking whether a coBüchi automaton is determinisable by pruning is NP-complete. On finite or infinite words, we show that computing the width of an automaton is EXPTIME-complete. This implies EXPTIME-completeness for multipebble simulation games on NFAs
Computing the Width of Non-deterministic Automata
We introduce a measure called width, quantifying the amount of nondeterminism
in automata. Width generalises the notion of good-for-games (GFG) automata,
that correspond to NFAs of width 1, and where an accepting run can be built
on-the-fly on any accepted input. We describe an incremental determinisation
construction on NFAs, which can be more efficient than the full powerset
determinisation, depending on the width of the input NFA. This construction can
be generalised to infinite words, and is particularly well-suited to coB\"uchi
automata. For coB\"uchi automata, this procedure can be used to compute either
a deterministic automaton or a GFG one, and it is algorithmically more
efficient in the last case. We show this fact by proving that checking whether
a coB\"uchi automaton is determinisable by pruning is NP-complete. On finite or
infinite words, we show that computing the width of an automaton is
EXPTIME-complete. This implies EXPTIME-completeness for multipebble simulation
games on NFAs
Communication Complexity with Small Advantage
We study problems in randomized communication complexity when the protocol is only required to attain some small advantage over purely random guessing, i.e., it produces the correct output with probability at least epsilon greater than one over the codomain size of the function. Previously, Braverman and Moitra (STOC 2013) showed that the set-intersection function requires Theta(epsilon n) communication to achieve advantage epsilon. Building on this, we prove the same bound for several variants of set-intersection: (1) the classic "tribes" function obtained by composing with And (provided 1/epsilon is at most the width of the And), and (2) the variant where the sets are uniquely intersecting and the goal is to determine partial information about (say, certain bits of the index of) the intersecting coordinate
A Parameterized Study of Maximum Generalized Pattern Matching Problems
The generalized function matching (GFM) problem has been intensively studied
starting with [Ehrenfeucht and Rozenberg, 1979]. Given a pattern p and a text
t, the goal is to find a mapping from the letters of p to non-empty substrings
of t, such that applying the mapping to p results in t. Very recently, the
problem has been investigated within the framework of parameterized complexity
[Fernau, Schmid, and Villanger, 2013].
In this paper we study the parameterized complexity of the optimization
variant of GFM (called Max-GFM), which has been introduced in [Amir and Nor,
2007]. Here, one is allowed to replace some of the pattern letters with some
special symbols "?", termed wildcards or don't cares, which can be mapped to an
arbitrary substring of the text. The goal is to minimize the number of
wildcards used.
We give a complete classification of the parameterized complexity of Max-GFM
and its variants under a wide range of parameterizations, such as, the number
of occurrences of a letter in the text, the size of the text alphabet, the
number of occurrences of a letter in the pattern, the size of the pattern
alphabet, the maximum length of a string matched to any pattern letter, the
number of wildcards and the maximum size of a string that a wildcard can be
mapped to.Comment: to appear in Proc. IPEC'1
Uniform Sampling for Networks of Automata
We call network of automata a family of partially synchronised automata, i.e. a family of deterministic automata which are synchronised via shared letters, and evolve independently otherwise. We address the problem of uniform random sampling of words recognised by a network of automata.
To that purpose, we define the reduced automaton of the model, which involves only the product of the synchronised part of the component automata. We provide uniform sampling algorithms which are polynomial with respect to the size of the reduced automaton, greatly improving on the best known algorithms. Our sampling algorithms rely on combinatorial and probabilistic methods and are of three different types: exact, Boltzmann and Parry sampling
An Efficient Representation for Filtrations of Simplicial Complexes
A filtration over a simplicial complex is an ordering of the simplices of
such that all prefixes in the ordering are subcomplexes of . Filtrations
are at the core of Persistent Homology, a major tool in Topological Data
Analysis. In order to represent the filtration of a simplicial complex, the
entire filtration can be appended to any data structure that explicitly stores
all the simplices of the complex such as the Hasse diagram or the recently
introduced Simplex Tree [Algorithmica '14]. However, with the popularity of
various computational methods that need to handle simplicial complexes, and
with the rapidly increasing size of the complexes, the task of finding a
compact data structure that can still support efficient queries is of great
interest.
In this paper, we propose a new data structure called the Critical Simplex
Diagram (CSD) which is a variant of the Simplex Array List (SAL) [Algorithmica
'17]. Our data structure allows one to store in a compact way the filtration of
a simplicial complex, and allows for the efficient implementation of a large
range of basic operations. Moreover, we prove that our data structure is
essentially optimal with respect to the requisite storage space. Finally, we
show that the CSD representation admits fast construction algorithms for Flag
complexes and relaxed Delaunay complexes.Comment: A preliminary version appeared in SODA 201