325 research outputs found
On sets of numbers rationally represented in a rational base number system
In this work, it is proved that a set of numbers closed under addition and
whose representations in a rational base numeration system is a rational
language is not a finitely generated additive monoid.
A key to the proof is the definition of a strong combinatorial property on
languages : the bounded left iteration property. It is both an unnatural
property in usual formal language theory (as it contradicts any kind of pumping
lemma) and an ideal fit to the languages defined through rational base number
systems
Principal AFL
A (full) principal AFL is a (full) AFL generated by a single language, i.e., it is thesmallest (full) AFL containing the given language. In the present paper, a study is made of such AFL. First, an AFA (abstract family of acceptors) characterization of (full) principal AFL is given. From this result, many well-known families of AFL can be shown to be (full) principal AFL. Next, two representation theorems for each language in a (full) principal AFL are given. The first involves the generator and one application each of concatenation, star, intersection with a regular set, inverse homomorphism, and a special type of homomorphism. The second involves an a-transducer, the generator, and one application of concatenation and star. Finally, it is shown that if â1 and â2 are (full) principal AFL, then so are (a) the smallest (full) AFL containing {L1â©L2/L1 in â1, L2 in â2 and (b) the family obtained by substituting Δ-free languages of â2 into languages of â1
Reset machines
AbstractA reset tape has one read-write head which moves only left-to-right except that the head can be reset once to the left end and the tape rescanned; a multiple-reset machine has reset tapes as auxiliary storage and a one-way input tape. Linear time is no more powerful than real time for nondeterministic multiple-reset machines and so the family MULTI-RESET of languages accepted in real time by nondeterministic multiple-reset machines is closed under linear erasing. MULTI-RESET is closed under Kleene. It can be characterized as the smallest family of languages containing the regular sets and closed under intersection and linear-erasing homomorphic duplication or as the smallest intersection-closed semiAFL containing COPY = {ww | w in {a, b}â}. A circular tape is read full-sweep from left-to-right only and then reset to the left, any number of times; a nonwriting circular tape cannot be altered after the first sweep. For nondeterministic machines operating in real time, multiple reset tapes, circular tapes or nonwriting circular tapes have the same power. Languages in MULTI-RESET can be accepted in real time by nondeterministic machines using only three reset tapes or using only one reset tape and one nonwriting circular tape
Decidability of strong equivalence for subschemas of a class of linear, free, near-liberal program schemas
The article attached is a preprint version of the final published article which can be accessed at the link below. The article title has been changed. For referencing purposes please use the published details. Copyright © 2010 Elsevier B.V. All rights reserved.A program schema defines a class of programs, all of which have identical statement structure, but whose functions and predicates may differ. A schema thus defines an entire class of programs according to how its symbols are interpreted. Two schemas are strongly equivalent if they always define the same function from initial states to final states for every interpretation. A subschema of a schema is obtained from a schema by deleting some of its statements. A schema S is liberal if there exists an initial state in the Herbrand domain such that the same term is not generated more than once along any executable path through S. In this paper, we introduce near-liberal schemas, in which this non-repeating condition applies only to terms not having the form g() for a constant function symbol g. Given a schema S that is linear (no function or predicate symbol occurs more than once in S) and a variable v, we compute a set of function and predicate symbols in S which is a subset of those defined by Weiser's slicing algorithm and prove that if for every while predicate q in S and every constant assignment w:=g(); lying in the body of q, no other assignment to w also lies in the body of q, our smaller symbol set defines a correct subschema of S with respect to the final value of v after execution. We also prove that if S is also free (every path through S is executable) and near-liberal, it is decidable which of its subschemas are strongly equivalent to S. For the class of pairs of schemas in which one schema is a subschema of the other, this generalises a recent result in which S was required to be linear, free and liberal.This work was supported by a grant from the Engineering and Physical Sciences Research Council, Grant EP/E002919/1
Characterizing minimal semantics-preserving slices of predicate-linear, free, liberal program schemas
This is a preprint version of the article - Copyright @ 2011 ElsevierA program schema defines a class of programs, all of which have identical statement structure, but whose functions and predicates may differ. A schema thus defines an entire class of programs according to how its symbols are interpreted. A subschema of a schema is obtained from a schema by deleting some of its statements. We prove that given a schema S which is predicate-linear, free and liberal, such that the true and false parts of every if predicate satisfy a simple additional condition, and a slicing criterion defined by the final value of a given variable after execution of any program defined by S, the minimal subschema of S which respects this slicing criterion contains all the function and predicate symbols âneededâ by the variable according to the data dependence and control dependence relations used in program slicing, which is the symbol set given by Weiserâs static slicing algorithm. Thus this algorithm gives predicate-minimal slices for classes of programs represented by schemas satisfying our set of conditions. We also give an example to show that the corresponding result with respect to the slicing criterion defined by termination behaviour is incorrect. This complements a result by the authors in which S was required to be function-linear, instead of predicate-linear.This work was supported by a grant from the Engineering and Physical Sciences Research Council, Grant EP/E002919/1
Bounded Counter Languages
We show that deterministic finite automata equipped with two-way heads
are equivalent to deterministic machines with a single two-way input head and
linearly bounded counters if the accepted language is strictly bounded,
i.e., a subset of for a fixed sequence of symbols . Then we investigate linear speed-up for counter machines. Lower
and upper time bounds for concrete recognition problems are shown, implying
that in general linear speed-up does not hold for counter machines. For bounded
languages we develop a technique for speeding up computations by any constant
factor at the expense of adding a fixed number of counters
Real-Time Vector Automata
We study the computational power of real-time finite automata that have been
augmented with a vector of dimension k, and programmed to multiply this vector
at each step by an appropriately selected matrix. Only one entry
of the vector can be tested for equality to 1 at any time. Classes of languages
recognized by deterministic, nondeterministic, and "blind" versions of these
machines are studied and compared with each other, and the associated classes
for multicounter automata, automata with multiplication, and generalized finite
automata.Comment: 14 page
Regular realizability problems and context-free languages
We investigate regular realizability (RR) problems, which are the problems of
verifying whether intersection of a regular language -- the input of the
problem -- and fixed language called filter is non-empty. In this paper we
focus on the case of context-free filters. Algorithmic complexity of the RR
problem is a very coarse measure of context-free languages complexity. This
characteristic is compatible with rational dominance. We present examples of
P-complete RR problems as well as examples of RR problems in the class NL. Also
we discuss RR problems with context-free filters that might have intermediate
complexity. Possible candidates are the languages with polynomially bounded
rational indices.Comment: conference DCFS 201
Parikh's Theorem: A simple and direct automaton construction
Parikh's theorem states that the Parikh image of a context-free language is
semilinear or, equivalently, that every context-free language has the same
Parikh image as some regular language. We present a very simple construction
that, given a context-free grammar, produces a finite automaton recognizing
such a regular language.Comment: 12 pages, 3 figure
Silent Transitions in Automata with Storage
We consider the computational power of silent transitions in one-way automata
with storage. Specifically, we ask which storage mechanisms admit a
transformation of a given automaton into one that accepts the same language and
reads at least one input symbol in each step.
We study this question using the model of valence automata. Here, a finite
automaton is equipped with a storage mechanism that is given by a monoid.
This work presents generalizations of known results on silent transitions.
For two classes of monoids, it provides characterizations of those monoids that
allow the removal of \lambda-transitions. Both classes are defined by graph
products of copies of the bicyclic monoid and the group of integers. The first
class contains pushdown storages as well as the blind counters while the second
class contains the blind and the partially blind counters.Comment: 32 pages, submitte
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