scholarly journals Digraph complexity measures and applications in formal language theory

2012 ◽  
Vol Vol. 14 no. 2 (Automata, Logic and Semantics) ◽  
Author(s):  
Hermann Gruber
Keyword(s):  
Polynomial Time ◽  
Formal Language ◽  
Regular Languages ◽  
Formal Language Theory ◽  
Language Theory ◽  
Complexity Measures ◽  
Time Approximation ◽  
Np Complete ◽  
Cycle Rank ◽  
Polynomial Time Approximation

Automata, Logic and Semantics International audience We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages. We explore this connection, and obtain several new algorithmic insights regarding both cycle rank and star height. Among other results, we show that computing the cycle rank is NP-complete, even for sparse digraphs of maximum outdegree 2. Notwithstanding, we provide both a polynomial-time approximation algorithm and an exponential-time exact algorithm for this problem. The former algorithm yields an O((log n)^(3/2))- approximation in polynomial time, whereas the latter yields the optimum solution, and runs in time and space O*(1.9129^n) on digraphs of maximum outdegree at most two. Regarding the star height problem, we identify a subclass of the regular languages for which we can precisely determine the computational complexity of the star height problem. Namely, the star height problem for bideterministic languages is NP-complete, and this holds already for binary alphabets. Then we translate the algorithmic results concerning cycle rank to the bideterministic star height problem, thus giving a polynomial-time approximation as well as a reasonably fast exact exponential algorithm for bideterministic star height.

scholarly journals Phonological typology in Optimality Theory and Formal Language Theory: goals and future directions

Phonology ◽  
2019 ◽  
Vol 36 (2) ◽  
pp. 351-353
Author(s):  
Joe Pater
Keyword(s):  
Recent Work ◽  
Optimality Theory ◽  
Formal Language ◽  
Regular Languages ◽  
Formal Language Theory ◽  
Language Theory ◽  
Future Directions ◽  
Chomsky Hierarchy ◽  
Phonological Typology

Much recent work has studied phonological typology in terms of Formal Language Theory (e.g. the Chomsky hierarchy). This paper considers whether Optimality Theory grammars might be constrained to generate only regular languages, and also whether the tools of formal language theory might be used for constructing phonological theories similar to those within Optimality Theory. It offers reasons to be optimistic about the first possibility, and sceptical about the second.

scholarly journals Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
M. Bouznif ◽  
R. Giroudeau
Keyword(s):  
Approximation Algorithm ◽  
Large Class ◽  
Bipartite Graph ◽  
Polynomial Time ◽  
Performance Guarantee ◽  
Makespan Minimization ◽  
Time Approximation ◽  
Polynomial Time Approximation Algorithm ◽  
Precedence Graph ◽  
Polynomial Time Approximation

We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fixed diameter . We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time -approximation algorithm for the makespan minimization on processor networks with diameter .

THE DEVELOPMENT OF FORMAL LANGUAGE THEORY SINCE 1956

1990 ◽  
Vol 01 (04) ◽  
pp. 355-368
Author(s):  
ROBERT McNAUGHTON
Keyword(s):  
Formal Language ◽  
Formal Languages ◽  
Early Years ◽  
Formal Language Theory ◽  
Language Theory ◽  
Personal Interest

This brief survey will discuss the early years of the theory of formal languages through about 1970, treating only the most fundamental of the concepts. The paper will conclude with a brief discussion of a small number of topics, the choice reflecting only the personal interest of the author.

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