22 research outputs found
On Pebble Automata for Data Languages with Decidable Emptiness Problem
In this paper we study a subclass of pebble automata (PA) for data languages
for which the emptiness problem is decidable. Namely, we introduce the
so-called top view weak PA. Roughly speaking, top view weak PA are weak PA
where the equality test is performed only between the data values seen by the
two most recently placed pebbles. The emptiness problem for this model is
decidable. We also show that it is robust: alternating, nondeterministic and
deterministic top view weak PA have the same recognition power. Moreover, this
model is strong enough to accept all data languages expressible in Linear
Temporal Logic with the future-time operators, augmented with one register
freeze quantifier.Comment: An extended abstract of this work has been published in the
proceedings of the 34th International Symposium on Mathematical Foundations
of Computer Science (MFCS) 2009}, Springer, Lecture Notes in Computer Science
5734, pages 712-72
The power of writing, a pebble hierarchy and a narrative for the teaching of Automata Theory
In this work we study pebble automata. Those automata constitute an infinite hierarchy of discrete models of computation. The hierarchy begins at the level of finite state automata (0-pebble automata) and approaches the model of onetape Turing machines. Thus, it can be argued that it is a complete hierarchy that covers, in a continuous way, all the models of automata that are important in the theory of computation. We investigate the use of this hierarchy as a narrative for the teaching of automata theory. We also investigate some fundamental questions concerning the power of pebble automata.Sociedad Argentina de Informática e Investigación Operativa (SADIO
Translation from Classical Two-Way Automata to Pebble Two-Way Automata
We study the relation between the standard two-way automata and more powerful
devices, namely, two-way finite automata with an additional "pebble" movable
along the input tape. Similarly as in the case of the classical two-way
machines, it is not known whether there exists a polynomial trade-off, in the
number of states, between the nondeterministic and deterministic pebble two-way
automata. However, we show that these two machine models are not independent:
if there exists a polynomial trade-off for the classical two-way automata, then
there must also exist a polynomial trade-off for the pebble two-way automata.
Thus, we have an upward collapse (or a downward separation) from the classical
two-way automata to more powerful pebble automata, still staying within the
class of regular languages. The same upward collapse holds for complementation
of nondeterministic two-way machines.
These results are obtained by showing that each pebble machine can be, by
using suitable inputs, simulated by a classical two-way automaton with a linear
number of states (and vice versa), despite the existing exponential blow-up
between the classical and pebble two-way machines
Automata with modulo counters and nondeterministic counter bounds
We introduce and investigate Nondeterministically Bounded
Modulo Counter Automata (NBMCA), which are two-way one-head automata
that comprise a constant number of modulo counters, where the
counter bounds are nondeterministically guessed, and this is the only
element of nondeterminism. NBMCA are tailored to recognising those
languages that are characterised by the existence of a specific factorisation
of their words, e. g., pattern languages. In this work, we subject
NBMCA to a theoretically sound analysis
Temporal Logics on Words with Multiple Data Values
The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)-pairs at each position. It considers a basic logic which is a semantical fragment of the logic of Demri and Lazic with operators for navigation into the future and the past. By reduction to the emptiness problem for data automata it is shown that this basic logic is decidable. Whereas the basic logic only allows navigation to positions where a fixed data value occurs, extensions are studied that also allow navigation to positions with different data values. Besides some undecidable results it is shown that the extension by a certain UNTIL-operator with an inequality target condition remains decidable
The power of writing, a pebble hierarchy and a narrative for the teaching of Automata Theory
In this work we study pebble automata. Those automata constitute an infinite hierarchy of discrete models of computation. The hierarchy begins at the level of finite state automata (0-pebble automata) and approaches the model of onetape Turing machines. Thus, it can be argued that it is a complete hierarchy that covers, in a continuous way, all the models of automata that are important in the theory of computation. We investigate the use of this hierarchy as a narrative for the teaching of automata theory. We also investigate some fundamental questions concerning the power of pebble automata.Sociedad Argentina de Informática e Investigación Operativa (SADIO
Some properties of one-pebble Turing machines with sublogarithmic space
AbstractThis paper investigates some aspects of the accepting powers of deterministic, nondeterministic, and alternating one-pebble Turing machines with spaces between loglogn and logn. We first investigate a relationship between the accepting powers of two-way deterministic one-counter automata and deterministic (or nondeterministic) one-pebble Turing machines, and show that they are incomparable. Then we investigate a relationship between nondeterminism and alternation, and show that there exists a language accepted by a strongly loglogn space-bounded alternating one-pebble Turing machine, but not accepted by any weakly o(logn) space-bounded nondeterministic one-pebble Turing machine. Finally, we investigate a space hierarchy, and show that for any one-pebble (fully) space constructible function L(n)⩽logn, and for any function L′(n)=o(L(n)), there exists a language accepted by a strongly L(n) space-bounded deterministic one-pebble Turing machine, but not accepted by any weakly L′(n) space-bounded nondeterministic one-pebble Turing machine
Complexity Hierarchies Beyond Elementary
We introduce a hierarchy of fast-growing complexity classes and show its
suitability for completeness statements of many non elementary problems. This
hierarchy allows the classification of many decision problems with a
non-elementary complexity, which occur naturally in logic, combinatorics,
formal languages, verification, etc., with complexities ranging from simple
towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep
updating the catalogue of problems from Section 6 in future revision
Logic Meets Algebra: the Case of Regular Languages
The study of finite automata and regular languages is a privileged meeting
point of algebra and logic. Since the work of Buchi, regular languages have
been classified according to their descriptive complexity, i.e. the type of
logical formalism required to define them. The algebraic point of view on
automata is an essential complement of this classification: by providing
alternative, algebraic characterizations for the classes, it often yields the
only opportunity for the design of algorithms that decide expressibility in
some logical fragment.
We survey the existing results relating the expressibility of regular
languages in logical fragments of MSO[S] with algebraic properties of their
minimal automata. In particular, we show that many of the best known results in
this area share the same underlying mechanics and rely on a very strong
relation between logical substitutions and block-products of pseudovarieties of
monoid. We also explain the impact of these connections on circuit complexity
theory.Comment: 37 page
Set Augmented Finite Automata over Infinite Alphabets
A data language is a set of finite words defined on an infinite alphabet.
Data languages are used to express properties associated with data values
(domain defined over a countably infinite set). In this paper, we introduce set
augmented finite automata (SAFA), a new class of automata for expressing data
languages. We investigate the decision problems, closure properties, and
expressiveness of SAFA. We also study the deterministic variant of these
automata.Comment: This is a full version of a paper with the same name accepted in DLT
2023. Other than the full proofs, this paper contains several new results
concerning more closure properties, universality problem, comparison of
expressiveness with register automata and class counter automata, and more
results on deterministic SAF