1,026 research outputs found
Weighted Logics for Nested Words and Algebraic Formal Power Series
Nested words, a model for recursive programs proposed by Alur and Madhusudan,
have recently gained much interest. In this paper we introduce quantitative
extensions and study nested word series which assign to nested words elements
of a semiring. We show that regular nested word series coincide with series
definable in weighted logics as introduced by Droste and Gastin. For this we
establish a connection between nested words and the free bisemigroup. Applying
our result, we obtain characterizations of algebraic formal power series in
terms of weighted logics. This generalizes results of Lautemann, Schwentick and
Therien on context-free languages
MSO definable string transductions and two-way finite state transducers
String transductions that are definable in monadic second-order (mso) logic
(without the use of parameters) are exactly those realized by deterministic
two-way finite state transducers. Nondeterministic mso definable string
transductions (i.e., those definable with the use of parameters) correspond to
compositions of two nondeterministic two-way finite state transducers that have
the finite visit property. Both families of mso definable string transductions
are characterized in terms of Hennie machines, i.e., two-way finite state
transducers with the finite visit property that are allowed to rewrite their
input tape.Comment: 63 pages, LaTeX2e. Extended abstract presented at 26-th ICALP, 199
Complete Axiomatizations of Fragments of Monadic Second-Order Logic on Finite Trees
We consider a specific class of tree structures that can represent basic
structures in linguistics and computer science such as XML documents, parse
trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We
present axiomatizations of the monadic second-order logic (MSO), monadic
transitive closure logic (FO(TC1)) and monadic least fixed-point logic
(FO(LFP1)) theories of this class of structures. These logics can express
important properties such as reachability. Using model-theoretic techniques, we
show by a uniform argument that these axiomatizations are complete, i.e., each
formula that is valid on all finite trees is provable using our axioms. As a
backdrop to our positive results, on arbitrary structures, the logics that we
study are known to be non-recursively axiomatizable
Playing Games in the Baire Space
We solve a generalized version of Church's Synthesis Problem where a play is
given by a sequence of natural numbers rather than a sequence of bits; so a
play is an element of the Baire space rather than of the Cantor space. Two
players Input and Output choose natural numbers in alternation to generate a
play. We present a natural model of automata ("N-memory automata") equipped
with the parity acceptance condition, and we introduce also the corresponding
model of "N-memory transducers". We show that solvability of games specified by
N-memory automata (i.e., existence of a winning strategy for player Output) is
decidable, and that in this case an N-memory transducer can be constructed that
implements a winning strategy for player Output.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017
Tarski's influence on computer science
The influence of Alfred Tarski on computer science was indirect but
significant in a number of directions and was in certain respects fundamental.
Here surveyed is the work of Tarski on the decision procedure for algebra and
geometry, the method of elimination of quantifiers, the semantics of formal
languages, modeltheoretic preservation theorems, and algebraic logic; various
connections of each with computer science are taken up
Two-Way Visibly Pushdown Automata and Transducers
Automata-logic connections are pillars of the theory of regular languages.
Such connections are harder to obtain for transducers, but important results
have been obtained recently for word-to-word transformations, showing that the
three following models are equivalent: deterministic two-way transducers,
monadic second-order (MSO) transducers, and deterministic one-way automata
equipped with a finite number of registers. Nested words are words with a
nesting structure, allowing to model unranked trees as their depth-first-search
linearisations. In this paper, we consider transformations from nested words to
words, allowing in particular to produce unranked trees if output words have a
nesting structure. The model of visibly pushdown transducers allows to describe
such transformations, and we propose a simple deterministic extension of this
model with two-way moves that has the following properties: i) it is a simple
computational model, that naturally has a good evaluation complexity; ii) it is
expressive: it subsumes nested word-to-word MSO transducers, and the exact
expressiveness of MSO transducers is recovered using a simple syntactic
restriction; iii) it has good algorithmic/closure properties: the model is
closed under composition with a unambiguous one-way letter-to-letter transducer
which gives closure under regular look-around, and has a decidable equivalence
problem
- …