59 research outputs found
On Languages Accepted by P/T Systems Composed of joins
Recently, some studies linked the computational power of abstract computing
systems based on multiset rewriting to models of Petri nets and the computation
power of these nets to their topology. In turn, the computational power of
these abstract computing devices can be understood by just looking at their
topology, that is, information flow.
Here we continue this line of research introducing J languages and proving
that they can be accepted by place/transition systems whose underlying net is
composed only of joins. Moreover, we investigate how J languages relate to
other families of formal languages. In particular, we show that every J
language can be accepted by a log n space-bounded non-deterministic Turing
machine with a one-way read-only input. We also show that every J language has
a semilinear Parikh map and that J languages and context-free languages (CFLs)
are incomparable
Matrix Languages, Register Machines, Vector Addition Systems
We give a direct and simple proof of the equality of Parikh images of lan-
guages generated by matrix grammars with appearance checking with the sets of vectors
generated by register machines. As a particular case, we get the equality of the Parikh
images of languages generated by matrix grammars without appearance checking with
the sets of vectors generated by partially blind register machines. Then, we consider pure
matrix grammars (i.e., grammars which do not distinguish terminal and nonterminal
symbols), and prove the inclusion of the family of Parikh images of languages generated
by such grammars (without appearance checking) in the family of sets of vectors generated by blind register machines, as well as the inclusion of reachability sets of vector
addition systems in the family of Parikh images of pure matrix languages. For pure matrix grammars with a certain restriction on the form of matrices, also the converse of the
latter inclusion is obtained. Thus, in view of the result from, we obtain the semilin-
earity of languages generated by pure matrix grammars (without appearance checking)
with alphabets with at most five letters, with the considered restrictions on the form of
matrices. A pure matrix grammar with five symbols, but without restrictions on the form
of matrices, is produced which generates a non-semilinear language
Relationships Between Bounded Languages, Counter Machines, Finite-Index Grammars, Ambiguity, and Commutative Equivalence
It is shown that for every language family that is a trio containing only semilinear languages, all bounded languages in it can be accepted by one-way deterministic reversal-bounded multicounter machines (DCM). This implies that for every semilinear trio (where these properties are effective), it is possible to decide containment, equivalence, and disjointness concerning its bounded languages. A condition is also provided for when the bounded languages in a semilinear trio coincide exactly with those accepted by DCM machines, and it is used to show that many grammar systems of finite index — such as finite-index matrix grammars (Mfin) and finite-index ET0L (ET0Lfin) — have identical bounded languages as DCM. Then connections between ambiguity, counting regularity, and commutative regularity are made, as many machines and grammars that are unambiguous can only generate/accept counting regular or com- mutatively regular languages. Thus, such a system that can generate/accept a non-counting regular or non-commutatively regular language implies the existence of inherently ambiguous languages over that system. In addition, it is shown that every language generated by an unambiguous Mfin has a rational char- acteristic series in commutative variables, and is counting regular. This result plus the connections are used to demonstrate that the grammar systems Mfin and ET0Lfin can generate inherently ambiguous languages (over their grammars), as do several machine models. It is also shown that all bounded languages generated by these two grammar systems (those in any semilinear trio) can be generated unambiguously within the systems. Finally, conditions on Mfin and ET0Lfin languages implying commutative regularity are obtained. In particular, it is shown that every finite-index ED0L language is commutatively regular
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg,
1966). Since that time, a vast literature on computational and descriptional
complexity issues on multi-head finite automata documenting the importance of
these devices has been developed. Although multi-head finite automata are a
simple concept, their computational behavior can be already very complex and
leads to undecidable or even non-semi-decidable problems on these devices such
as, for example, emptiness, finiteness, universality, equivalence, etc. These
strong negative results trigger the study of subclasses and alternative
characterizations of multi-head finite automata for a better understanding of
the nature of non-recursive trade-offs and, thus, the borderline between
decidable and undecidable problems. In the present paper, we tour a fragment of
this literature
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