986 research outputs found
Algebraic properties of structured context-free languages: old approaches and novel developments
The historical research line on the algebraic properties of structured CF
languages initiated by McNaughton's Parenthesis Languages has recently
attracted much renewed interest with the Balanced Languages, the Visibly
Pushdown Automata languages (VPDA), the Synchronized Languages, and the
Height-deterministic ones. Such families preserve to a varying degree the basic
algebraic properties of Regular languages: boolean closure, closure under
reversal, under concatenation, and Kleene star. We prove that the VPDA family
is strictly contained within the Floyd Grammars (FG) family historically known
as operator precedence. Languages over the same precedence matrix are known to
be closed under boolean operations, and are recognized by a machine whose pop
or push operations on the stack are purely determined by terminal letters. We
characterize VPDA's as the subclass of FG having a peculiarly structured set of
precedence relations, and balanced grammars as a further restricted case. The
non-counting invariance property of FG has a direct implication for VPDA too.Comment: Extended version of paper presented at WORDS2009, Salerno,Italy,
September 200
Precedence Automata and Languages
Operator precedence grammars define a classical Boolean and deterministic
context-free family (called Floyd languages or FLs). FLs have been shown to
strictly include the well-known visibly pushdown languages, and enjoy the same
nice closure properties. We introduce here Floyd automata, an equivalent
operational formalism for defining FLs. This also permits to extend the class
to deal with infinite strings to perform for instance model checking.Comment: Extended version of the paper which appeared in Proceedings of CSR
2011, Lecture Notes in Computer Science, vol. 6651, pp. 291-304, 2011.
Theorem 1 has been corrected and a complete proof is given in Appendi
On Measuring Non-Recursive Trade-Offs
We investigate the phenomenon of non-recursive trade-offs between
descriptional systems in an abstract fashion. We aim at categorizing
non-recursive trade-offs by bounds on their growth rate, and show how to deduce
such bounds in general. We also identify criteria which, in the spirit of
abstract language theory, allow us to deduce non-recursive tradeoffs from
effective closure properties of language families on the one hand, and
differences in the decidability status of basic decision problems on the other.
We develop a qualitative classification of non-recursive trade-offs in order to
obtain a better understanding of this very fundamental behaviour of
descriptional systems
Unary Pushdown Automata and Straight-Line Programs
We consider decision problems for deterministic pushdown automata over a
unary alphabet (udpda, for short). Udpda are a simple computation model that
accept exactly the unary regular languages, but can be exponentially more
succinct than finite-state automata. We complete the complexity landscape for
udpda by showing that emptiness (and thus universality) is P-hard, equivalence
and compressed membership problems are P-complete, and inclusion is
coNP-complete. Our upper bounds are based on a translation theorem between
udpda and straight-line programs over the binary alphabet (SLPs). We show that
the characteristic sequence of any udpda can be represented as a pair of
SLPs---one for the prefix, one for the lasso---that have size linear in the
size of the udpda and can be computed in polynomial time. Hence, decision
problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP
can be converted in logarithmic space into a udpda, and this forms the basis
for our lower bound proofs. We show coNP-hardness of the ordered matching
problem for SLPs, from which we derive coNP-hardness for inclusion. In
addition, we complete the complexity landscape for unary nondeterministic
pushdown automata by showing that the universality problem is -hard, using a new class of integer expressions. Our techniques have
applications beyond udpda. We show that our results imply -completeness for a natural fragment of Presburger arithmetic and coNP lower
bounds for compressed matching problems with one-character wildcards
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
Partially-commutative context-free languages
The paper is about a class of languages that extends context-free languages
(CFL) and is stable under shuffle. Specifically, we investigate the class of
partially-commutative context-free languages (PCCFL), where non-terminal
symbols are commutative according to a binary independence relation, very much
like in trace theory. The class has been recently proposed as a robust class
subsuming CFL and commutative CFL. This paper surveys properties of PCCFL. We
identify a natural corresponding automaton model: stateless multi-pushdown
automata. We show stability of the class under natural operations, including
homomorphic images and shuffle. Finally, we relate expressiveness of PCCFL to
two other relevant classes: CFL extended with shuffle and trace-closures of
CFL. Among technical contributions of the paper are pumping lemmas, as an
elegant completion of known pumping properties of regular languages, CFL and
commutative CFL.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
Generalizing input-driven languages: theoretical and practical benefits
Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks
to their simplicity they enjoy various nice algebraic and logic properties that
have been successfully exploited in many application fields. Practically all of
their related problems are decidable, so that they support automatic
verification algorithms. Also, they can be recognized in real-time.
Context-free languages (CFL) are another major family well-suited to
formalize programming, natural, and many other classes of languages; their
increased generative power w.r.t. RL, however, causes the loss of several
closure properties and of the decidability of important problems; furthermore
they need complex parsing algorithms. Thus, various subclasses thereof have
been defined with different goals, spanning from efficient, deterministic
parsing to closure properties, logic characterization and automatic
verification techniques.
Among CFL subclasses, so-called structured ones, i.e., those where the
typical tree-structure is visible in the sentences, exhibit many of the
algebraic and logic properties of RL, whereas deterministic CFL have been
thoroughly exploited in compiler construction and other application fields.
After surveying and comparing the main properties of those various language
families, we go back to operator precedence languages (OPL), an old family
through which R. Floyd pioneered deterministic parsing, and we show that they
offer unexpected properties in two fields so far investigated in totally
independent ways: they enable parsing parallelization in a more effective way
than traditional sequential parsers, and exhibit the same algebraic and logic
properties so far obtained only for less expressive language families
On the Complexity of the Equivalence Problem for Probabilistic Automata
Checking two probabilistic automata for equivalence has been shown to be a
key problem for efficiently establishing various behavioural and anonymity
properties of probabilistic systems. In recent experiments a randomised
equivalence test based on polynomial identity testing outperformed
deterministic algorithms. In this paper we show that polynomial identity
testing yields efficient algorithms for various generalisations of the
equivalence problem. First, we provide a randomized NC procedure that also
outputs a counterexample trace in case of inequivalence. Second, we show how to
check for equivalence two probabilistic automata with (cumulative) rewards. Our
algorithm runs in deterministic polynomial time, if the number of reward
counters is fixed. Finally we show that the equivalence problem for
probabilistic visibly pushdown automata is logspace equivalent to the
Arithmetic Circuit Identity Testing problem, which is to decide whether a
polynomial represented by an arithmetic circuit is identically zero.Comment: technical report for a FoSSaCS'12 pape
- …