scholarly journals The descriptional power of queue automata of constant length

2021 ◽  
Vol 58 (4) ◽  
pp. 335-356
Author(s):  
Sebastian Jakobi ◽  
Katja Meckel ◽  
Carlo Mereghetti ◽  
Beatrice Palano
Keyword(s):  
Blow Up ◽  
Regular Expressions ◽  
Constant Length ◽  
Straight Line ◽  
Constant Height ◽  
Double Exponential ◽  
Finite State ◽  
Pushdown Automata ◽  
Exponential Size ◽  
Straight Line Programs

AbstractWe consider the notion of a constant length queue automaton—i.e., a traditional queue automaton with a built-in constant limit on the length of its queue—as a formalism for representing regular languages. We show that the descriptional power of constant length queue automata greatly outperforms that of traditional finite state automata, of constant height pushdown automata, and of straight line programs for regular expressions, by providing optimal exponential and double-exponential size gaps. Moreover, we prove that constant height pushdown automata can be simulated by constant length queue automata paying only by a linear size increase, and that removing nondeterminism in constant length queue automata requires an optimal exponential size blow-up, against the optimal double-exponential cost for determinizing constant height pushdown automata. Finally, we investigate the size cost of implementing Boolean language operations on deterministic and nondeterministic constant length queue automata.

Non-Self-Embedding Grammars, Constant-Height Pushdown Automata, and Limited Automata

2020 ◽  
pp. 1-25
Author(s):  
Bruno Guillon ◽  
Giovanni Pighizzini ◽  
Luca Prigioniero
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
Deterministic Finite Automata ◽  
Polynomial Size ◽  
Constant Height ◽  
Double Exponential ◽  
Recursive Structures ◽  
Deterministic Formula ◽  
Context Free ◽  
Pushdown Automata

Non-self-embedding grammars are a restriction of context-free grammars which does not allow to describe recursive structures and, hence, which characterizes only the class of regular languages. A double exponential gap in size from non-self-embedding grammars to deterministic finite automata is known. The same size gap is also known from constant-height pushdown automata and [Formula: see text]-limited automata to deterministic finite automata. Constant-height pushdown automata and [Formula: see text]-limited automata are compared with non-self-embedding grammars. It is proved that non-self-embedding grammars and constant-height pushdown automata are polynomially related in size. Furthermore, a polynomial size simulation by [Formula: see text]-limited automata is presented. However, the converse transformation is proved to cost exponential. Finally, a different simulation shows that also the conversion of deterministic constant-height pushdown automata into deterministic [Formula: see text]-limited automata costs polynomial.

scholarly journals COMPRESSED MEMBERSHIP PROBLEMS FOR REGULAR EXPRESSIONS AND HIERARCHICAL AUTOMATA

2010 ◽  
Vol 21 (05) ◽  
pp. 817-841 ◽  
Author(s):  
MARKUS LOHREY
Keyword(s):  
Open Problem ◽  
Regular Languages ◽  
Regular Expressions ◽  
Membership Problem ◽  
Complexity Bounds ◽  
Straight Line ◽  
Membership Problems ◽  
Context Free ◽  
Straight Line Programs ◽  
Extended Regular Expressions

Membership problems for compressed strings in regular languages are investigated. Strings are represented by straight-line programs, i.e., context-free grammars that generate exactly one string. For the representation of regular languages, various formalisms with different degrees of succinctness (e.g., suitably extended regular expressions, hierarchical automata) are considered. Precise complexity bounds are derived. Among other results, it is shown that the compressed membership problem for regular expressions with intersection is PSPACE-complete. This solves an open problem of Plandowski and Rytter.

scholarly journals Succinctness of Descriptions of Context-Free, Regular, and Finite Languages

1978 ◽  
Vol 7 (84) ◽  
Author(s):  
Erik Meineche Schmidt
Keyword(s):  
Complexity Theory ◽  
Finite Automata ◽  
Regular Expressions ◽  
Exponential Time ◽  
Double Exponential ◽  
Context Free ◽  
Pushdown Automata

<p>This thesis analyzes the descriptional power of finite automata, regular expressions, pushdown automata, and certain generalized models of macro grammars. For finite automata and pushdown automata the emphasis is on ambiguity. It is shown that ambiguous nondeterminism allows more succinct definitions than unambiguous nondeterminism which in turn allows more succinct definitions than determinism. The succinctness gain is nonrecursive for pda's and nonpolynomial for finite automata.</p><p>The succinctness of regular expressions and macro grammars is measured in terms of complexity theory. It is shown that the inequivalence problem for Ol macro grammars generating finite languages is hard for nondeterministic double exponential time, and that the ''nonemptiness of complement'' problem for unambiguous regular expressions is in NP. This implies that unambiguous regular expressions are ''easier'' than general regular expressions (unless NP is equal to PSPACE).</p>

scholarly journals Solving string constraints with Regex-dependent functions through transducers with priorities and variables

2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-31
Author(s):  
Taolue Chen ◽  
Alejandro Flores-Lamas ◽  
Matthew Hague ◽  
Zhilei Han ◽  
Denghang Hu ◽  
...  
Keyword(s):  
Programming Languages ◽  
Formal Language ◽  
Formal Semantics ◽  
Symbolic Execution ◽  
Language Theory ◽  
Regular Expressions ◽  
Constraint Language ◽  
Straight Line ◽  
Finite State ◽  
Lazy Semantics

Regular expressions are a classical concept in formal language theory. Regular expressions in programming languages (RegEx) such as JavaScript, feature non-standard semantics of operators (e.g. greedy/lazy Kleene star), as well as additional features such as capturing groups and references. While symbolic execution of programs containing RegExes appeals to string solvers natively supporting important features of RegEx, such a string solver is hitherto missing. In this paper, we propose the first string theory and string solver that natively provides such support. The key idea of our string solver is to introduce a new automata model, called prioritized streaming string transducers (PSST), to formalize the semantics of RegEx-dependent string functions. PSSTs combine priorities, which have previously been introduced in prioritized finite-state automata to capture greedy/lazy semantics, with string variables as in streaming string transducers to model capturing groups. We validate the consistency of the formal semantics with the actual JavaScript semantics by extensive experiments. Furthermore, to solve the string constraints, we show that PSSTs enjoy nice closure and algorithmic properties, in particular, the regularity-preserving property (i.e., pre-images of regular constraints under PSSTs are regular), and introduce a sound sequent calculus that exploits these properties and performs propagation of regular constraints by means of taking post-images or pre-images. Although the satisfiability of the string constraint language is generally undecidable, we show that our approach is complete for the so-called straight-line fragment. We evaluate the performance of our string solver on over 195000 string constraints generated from an open-source RegEx library. The experimental results show the efficacy of our approach, drastically improving the existing methods (via symbolic execution) in both precision and efficiency.

scholarly journals A NEW LINEAR GENETIC PROGRAMMING APPROACH BASED ON STRAIGHT LINE PROGRAMS: SOME THEORETICAL AND EXPERIMENTAL ASPECTS

2009 ◽  
Vol 18 (05) ◽  
pp. 757-781 ◽  
Author(s):  
CÉSAR L. ALONSO ◽  
JOSÉ LUIS MONTAÑA ◽  
JORGE PUENTE ◽  
CRUZ ENRIQUE BORGES
Keyword(s):  
Data Structure ◽  
Genetic Programming ◽  
Computer Programs ◽  
Symbolic Regression ◽  
Programming Approach ◽  
Linear Genetic Programming ◽  
Straight Line ◽  
Structured Representations ◽  
Regression Problems ◽  
Straight Line Programs

Tree encodings of programs are well known for their representative power and are used very often in Genetic Programming. In this paper we experiment with a new data structure, named straight line program (slp), to represent computer programs. The main features of this structure are described, new recombination operators for GP related to slp's are introduced and a study of the Vapnik-Chervonenkis dimension of families of slp's is done. Experiments have been performed on symbolic regression problems. Results are encouraging and suggest that the GP approach based on slp's consistently outperforms conventional GP based on tree structured representations.

On the average-case complexity of underdetermined functions

2018 ◽  
Vol 28 (4) ◽  
pp. 201-221
Author(s):  
Aleksandr V. Chashkin
Keyword(s):  
Boolean Functions ◽  
Correct Order ◽  
Average Case ◽  
Case Complexity ◽  
Average Case Complexity ◽  
Straight Line ◽  
Straight Line Programs

Abstract The average-case complexity of computation of underdetermined functions by straight-line programs with conditional stop over the basis of all at most two-place Boolean functions is considered. Correct order estimates of the average-case complexity of functions with maximum average-case complexity among all underdetermined functions are derived depending on the degree of their determinacy, the size of their domain, and the size of their support.

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