181 research outputs found
Nondeterminism and Guarded Commands
The purpose of this paper is to discuss the relevance of nondeterminism in
computer science, with a special emphasis on Dijkstra's guarded commands
language.Comment: 34 pages. This is authors' version of Chapter 8 of the book K.R. Apt
and C.A.R. Hoare (editors), Edsger Wybe Dijkstra: His Life, Work, and Legacy,
volume 45 of ACM Books. ACM/Morgan & Claypool, 202
Computations and interaction
We enhance the notion of a computation of the classical theory of computing with the notion of interaction. In this way, we enhance a Turing machine as a model of computation to a Reactive Turing Machine that is an abstract model of a computer as it is used nowadays, always interacting with the user and the world
Reachability in Higher-Order-Counters
Higher-order counter automata (\HOCS) can be either seen as a restriction of
higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an
extension of counter automata to higher levels. We distinguish two principal
kinds of \HOCS: those that can test whether the topmost counter value is zero
and those which cannot.
We show that control-state reachability for level \HOCS with -test is
complete for \mbox{}-fold exponential space; leaving out the -test
leads to completeness for \mbox{}-fold exponential time. Restricting
\HOCS (without -test) to level , we prove that global (forward or
backward) reachability analysis is \PTIME-complete. This enhances the known
result for pushdown systems which are subsumed by level \HOCS without
-test.
We transfer our results to the formal language setting. Assuming that \PTIME
\subsetneq \PSPACE \subsetneq \mathbf{EXPTIME}, we apply proof ideas of
Engelfriet and conclude that the hierarchies of languages of \HOPS and of \HOCS
form strictly interleaving hierarchies. Interestingly, Engelfriet's
constructions also allow to conclude immediately that the hierarchy of
collapsible pushdown languages is strict level-by-level due to the existing
complexity results for reachability on collapsible pushdown graphs. This
answers an open question independently asked by Parys and by Kobayashi.Comment: Version with Full Proofs of a paper that appears at MFCS 201
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
The Surprising Computational Power of Nondeterministic Stack RNNs
Traditional recurrent neural networks (RNNs) have a fixed, finite number of
memory cells. In theory (assuming bounded range and precision), this limits
their formal language recognition power to regular languages, and in practice,
RNNs have been shown to be unable to learn many context-free languages (CFLs).
In order to expand the class of languages RNNs recognize, prior work has
augmented RNNs with a nondeterministic stack data structure, putting them on
par with pushdown automata and increasing their language recognition power to
CFLs. Nondeterminism is needed for recognizing all CFLs (not just deterministic
CFLs), but in this paper, we show that nondeterminism and the neural controller
interact to produce two more unexpected abilities. First, the nondeterministic
stack RNN can recognize not only CFLs, but also many non-context-free
languages. Second, it can recognize languages with much larger alphabet sizes
than one might expect given the size of its stack alphabet. Finally, to
increase the information capacity in the stack and allow it to solve more
complicated tasks with large alphabet sizes, we propose a new version of the
nondeterministic stack that simulates stacks of vectors rather than discrete
symbols. We demonstrate perplexity improvements with this new model on the Penn
Treebank language modeling benchmark.Comment: 20 pages, 7 figures. Submitted to ICLR 202
Towards a Uniform Theory of Effectful State Machines
Using recent developments in coalgebraic and monad-based semantics, we
present a uniform study of various notions of machines, e.g. finite state
machines, multi-stack machines, Turing machines, valence automata, and weighted
automata. They are instances of Jacobs' notion of a T-automaton, where T is a
monad. We show that the generic language semantics for T-automata correctly
instantiates the usual language semantics for a number of known classes of
machines/languages, including regular, context-free, recursively-enumerable and
various subclasses of context free languages (e.g. deterministic and real-time
ones). Moreover, our approach provides new generic techniques for studying the
expressivity power of various machine-based models.Comment: final version accepted by TOC
Real-time multipushdown and multicounter automata networks and hierarchies
Ph.D.William I. Grosk
Collapse Operation Increases Expressive Power of Deterministic Higher Order Pushdown Automata
We show that collapsible deterministic second level pushdown automata can recognize more languages than deterministic second level pushdown automata (without collapse). This implies that there exists a tree generated by a second level recursion scheme which is not generated by any second level safe recursion scheme
Solving Infinite Games in the Baire Space
Infinite games (in the form of Gale-Stewart games) are studied where a play
is a sequence of natural numbers chosen by two players in alternation, the
winning condition being a subset of the Baire space . We
consider such games defined by a natural kind of parity automata over the
alphabet , called -MSO-automata, where transitions are
specified by monadic second-order formulas over the successor structure of the
natural numbers. We show that the classical B\"uchi-Landweber Theorem (for
finite-state games in the Cantor space ) holds again for the present
games: A game defined by a deterministic parity -MSO-automaton is
determined, the winner can be computed, and an -MSO-transducer
realizing a winning strategy for the winner can be constructed.Comment: Minor revision. 26 pages, 1 figur
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