371 research outputs found
Learning Residual Finite-State Automata Using Observation Tables
We define a two-step learner for RFSAs based on an observation table by using
an algorithm for minimal DFAs to build a table for the reversal of the language
in question and showing that we can derive the minimal RFSA from it after some
simple modifications. We compare the algorithm to two other table-based ones of
which one (by Bollig et al. 2009) infers a RFSA directly, and the other is
another two-step learner proposed by the author. We focus on the criterion of
query complexity.Comment: In Proceedings DCFS 2010, arXiv:1008.127
Pre-Reduction Graph Products: Hardnesses of Properly Learning DFAs and Approximating EDP on DAGs
The study of graph products is a major research topic and typically concerns
the term , e.g., to show that . In this paper, we
study graph products in a non-standard form where is a
"reduction", a transformation of any graph into an instance of an intended
optimization problem. We resolve some open problems as applications.
(1) A tight -approximation hardness for the minimum
consistent deterministic finite automaton (DFA) problem, where is the
sample size. Due to Board and Pitt [Theoretical Computer Science 1992], this
implies the hardness of properly learning DFAs assuming (the
weakest possible assumption).
(2) A tight hardness for the edge-disjoint paths (EDP)
problem on directed acyclic graphs (DAGs), where denotes the number of
vertices.
(3) A tight hardness of packing vertex-disjoint -cycles for large .
(4) An alternative (and perhaps simpler) proof for the hardness of properly
learning DNF, CNF and intersection of halfspaces [Alekhnovich et al., FOCS 2004
and J. Comput.Syst.Sci. 2008]
Automata Tutor v3
Computer science class enrollments have rapidly risen in the past decade.
With current class sizes, standard approaches to grading and providing
personalized feedback are no longer possible and new techniques become both
feasible and necessary. In this paper, we present the third version of Automata
Tutor, a tool for helping teachers and students in large courses on automata
and formal languages. The second version of Automata Tutor supported automatic
grading and feedback for finite-automata constructions and has already been
used by thousands of users in dozens of countries. This new version of Automata
Tutor supports automated grading and feedback generation for a greatly extended
variety of new problems, including problems that ask students to create regular
expressions, context-free grammars, pushdown automata and Turing machines
corresponding to a given description, and problems about converting between
equivalent models - e.g., from regular expressions to nondeterministic finite
automata. Moreover, for several problems, this new version also enables
teachers and students to automatically generate new problem instances. We also
present the results of a survey run on a class of 950 students, which shows
very positive results about the usability and usefulness of the tool
Automata theory in nominal sets
We study languages over infinite alphabets equipped with some structure that
can be tested by recognizing automata. We develop a framework for studying such
alphabets and the ensuing automata theory, where the key role is played by an
automorphism group of the alphabet. In the process, we generalize nominal sets
due to Gabbay and Pitts
Architectures in parametric component-based systems: Qualitative and quantitative modelling
One of the key aspects in component-based design is specifying the software
architecture that characterizes the topology and the permissible interactions
of the components of a system. To achieve well-founded design there is need to
address both the qualitative and non-functional aspects of architectures. In
this paper we study the qualitative and quantitative formal modelling of
architectures applied on parametric component-based systems, that consist of an
unknown number of instances of each component. Specifically, we introduce an
extended propositional interaction logic and investigate its first-order level
which serves as a formal language for the interactions of parametric systems.
Our logics achieve to encode the execution order of interactions, which is a
main feature in several important architectures, as well as to model recursive
interactions. Moreover, we prove the decidability of equivalence,
satisfiability, and validity of first-order extended interaction logic
formulas, and provide several examples of formulas describing well-known
architectures. We show the robustness of our theory by effectively extending
our results for parametric weighted architectures. For this, we study the
weighted counterparts of our logics over a commutative semiring, and we apply
them for modelling the quantitative aspects of concrete architectures. Finally,
we prove that the equivalence problem of weighted first-order extended
interaction logic formulas is decidable in a large class of semirings, namely
the class (of subsemirings) of skew fields.Comment: 53 pages, 11 figure
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