9,139 research outputs found
Parsing Unary Boolean Grammars Using Online Convolution
In contrast to context-free grammars, the extension of these
grammars by explicit conjunction, the so-called conjunctive
grammars can generate (quite complicated) non-regular languages
over a single-letter alphabet (DLT 2007). Given these
expressibility results, we study the parsability of Boolean grammars,
an extension of context-free grammars by conjunction and negation,
over a unary alphabet and show that they can be parsed in time O(|G| log^2(n) M(n))
where M(n) is the time to multiply two n-bit integers. This multiplication
algorithm is transformed into a convolution algorithm which in turn is
converted to an online convolution algorithm which is used for the parsing
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
Descriptional complexity of cellular automata and decidability questions
We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata
On non-recursive trade-offs between finite-turn pushdown automata
It is shown that between one-turn pushdown automata (1-turn PDAs) and deterministic finite automata (DFAs) there will be savings concerning the size of description not bounded by any recursive function, so-called non-recursive tradeoffs. Considering the number of turns of the stack height as a consumable resource of PDAs, we can show the existence of non-recursive trade-offs between PDAs performing k+ 1 turns and k turns for k >= 1. Furthermore, non-recursive trade-offs are shown between arbitrary PDAs and PDAs which perform only a finite number of turns. Finally, several decidability questions are shown to be undecidable and not semidecidable
Sublinear Parallel Time Recognition of Tree Adjoining Language
A parallel algorithm is presented for recognizing the class of languages generated by tree adjoining grammars, a tree rewriting system which has applications in computational Linguistics. This class of languages is known to properly include all context-free languages; for example, the non-context-free sets {anbncn} and {ww) are in this class. It is shown that the recognition problem for tree adjoining languages can be solved by a concurrent-read, exclusive-write parallel random-access machine (CREW PRAM) in 0 (log2(n)) time using polynomially many processors. This extends a previous result for context-free languages
Stream Processing using Grammars and Regular Expressions
In this dissertation we study regular expression based parsing and the use of
grammatical specifications for the synthesis of fast, streaming
string-processing programs.
In the first part we develop two linear-time algorithms for regular
expression based parsing with Perl-style greedy disambiguation. The first
algorithm operates in two passes in a semi-streaming fashion, using a constant
amount of working memory and an auxiliary tape storage which is written in the
first pass and consumed by the second. The second algorithm is a single-pass
and optimally streaming algorithm which outputs as much of the parse tree as is
semantically possible based on the input prefix read so far, and resorts to
buffering as many symbols as is required to resolve the next choice. Optimality
is obtained by performing a PSPACE-complete pre-analysis on the regular
expression.
In the second part we present Kleenex, a language for expressing
high-performance streaming string processing programs as regular grammars with
embedded semantic actions, and its compilation to streaming string transducers
with worst-case linear-time performance. Its underlying theory is based on
transducer decomposition into oracle and action machines, and a finite-state
specialization of the streaming parsing algorithm presented in the first part.
In the second part we also develop a new linear-time streaming parsing
algorithm for parsing expression grammars (PEG) which generalizes the regular
grammars of Kleenex. The algorithm is based on a bottom-up tabulation algorithm
reformulated using least fixed points and evaluated using an instance of the
chaotic iteration scheme by Cousot and Cousot
Selection pressure and organizational cognition: implications for the social determinants of health
We model the effects of Schumperterian 'selecton pressures' -- in particular Apartheid and the neoliberal 'market economy' -- on organizational cognition in minority communities, given the special role of culture in human biology. Our focus is on the dual-function social networks by which culture is imposed and maintained on individuals and by which immediate patterns of opportunity and threat are recognized and given response. A mathematical model based on recent advances in complexity theory displays a joint cross-scale linkage of social, individual central nervous system, and immune cognition with external selection pressure through mixed and synergistic punctuated 'learning plateaus.' This provides a natural mechanism for addressing the social determinants of health at the individual level. The implications of the model, particularly the predictions of synergistic punctuation, appear to be empirically testable
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