UNWEIGHTED AND WEIGHTED HYPER-MINIMIZATION

Hyper-minimization of deterministic finite automata (DFA) is a recently introduced state reduction technique that allows a finite change in the recognized language. A generalization of this lossy compression method to the weighted setting over semifields is presented, which allows the recognized weighted language to differ for finitely many input strings. First, the structure of hyper-minimal deterministic weighted finite automata is characterized in a similar way as in classical weighted minimization and unweighted hyper-minimization. Second, an efficient hyper-minimization algorithm, which runs in time [Formula: see text], is derived from this characterization. Third, the closure properties of canonical regular languages, which are languages recognized by hyper-minimal DFA, are investigated. Finally, some recent results in the area of hyper-minimization are recalled.

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Space-bounded OTMs and REG ∞

Computability ◽

10.3233/com-200327 ◽

2021 ◽

pp. 1-16

Author(s):

Merlin Carl

Keyword(s):

Complexity Theory ◽

Turing Machine ◽

Finite Automata ◽

Regular Languages ◽

The Other ◽

Deterministic Finite Automata ◽

Logarithmic Space ◽

Working Space ◽

Important Theorem

An important theorem in classical complexity theory is that REG = LOGLOGSPACE, i.e., that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce deterministic ordinal automata (DOAs) and show that they satisfy many of the basic statements of the theory of deterministic finite automata and regular languages. We then consider languages decidable by an ordinal Turing machine (OTM), introduced by P. Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA, which is a transfinite analogue of LOGLOGSPACE ⊆ REG; the other direction, however, is easily seen to fail.

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STATE COMPLEXITY OF ADDITIVE WEIGHTED FINITE AUTOMATA

International Journal of Foundations of Computer Science ◽

10.1142/s0129054107005443 ◽

2007 ◽

Vol 18 (06) ◽

pp. 1407-1416 ◽

Cited By ~ 10

Author(s):

KAI SALOMAA ◽

PAUL SCHOFIELD

Keyword(s):

Upper Bound ◽

Finite Automaton ◽

Regular Language ◽

Finite Automata ◽

The State ◽

Deterministic Finite Automata ◽

State Complexity ◽

Weighted Finite Automata

It is known that the neighborhood of a regular language with respect to an additive distance is regular. We introduce an additive weighted finite automaton model that provides a conceptually simple way to reprove this result. We consider the state complexity of converting additive weighted finite automata to deterministic finite automata. As our main result we establish a tight upper bound for the state complexity of the conversion.

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Nondeterministic Syntactic Complexity

Lecture Notes in Computer Science - Foundations of Software Science and Computation Structures ◽

10.1007/978-3-030-71995-1_23 ◽

2021 ◽

pp. 448-468

Author(s):

Robert S. R. Myers ◽

Stefan Milius ◽

Henning Urbat

Keyword(s):

Finite Automata ◽

Regular Languages ◽

Syntactic Complexity ◽

Deterministic Finite Automata ◽

Syntactic Monoid ◽

Nondeterministic Finite Automata ◽

Structural Work ◽

Algebraic Interpretation ◽

Nondeterministic State

AbstractWe introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the ‘canonical boolean representation’ of the syntactic monoid. Equivalently, it is the least number of states of any subatomic nondeterministic acceptor. It turns out that essentially all previous structural work on nondeterministic state-minimality computes this measure. Our approach rests on an algebraic interpretation of nondeterministic finite automata as deterministic finite automata endowed with semilattice structure. Crucially, the latter form a self-dual category.

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Reversible parallel communicating finite automata systems

Acta Informatica ◽

10.1007/s00236-021-00396-9 ◽

2021 ◽

Vol 58 (4) ◽

pp. 263-279

Author(s):

Henning Bordihn ◽

György Vaszil

Keyword(s):

Finite Automata ◽

Regular Languages ◽

The Other ◽

Deterministic Case ◽

Computational Power ◽

Deterministic Finite Automata ◽

Relationship Of ◽

The Relationship ◽

Context Free

AbstractWe study the concept of reversibility in connection with parallel communicating systems of finite automata (PCFA in short). We define the notion of reversibility in the case of PCFA (also covering the non-deterministic case) and discuss the relationship of the reversibility of the systems and the reversibility of its components. We show that a system can be reversible with non-reversible components, and the other way around, the reversibility of the components does not necessarily imply the reversibility of the system as a whole. We also investigate the computational power of deterministic centralized reversible PCFA. We show that these very simple types of PCFA (returning or non-returning) can recognize regular languages which cannot be accepted by reversible (deterministic) finite automata, and that they can even accept languages that are not context-free. We also separate the deterministic and non-deterministic variants in the case of systems with non-returning communication. We show that there are languages accepted by non-deterministic centralized PCFA, which cannot be recognized by any deterministic variant of the same type.

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Ambiguity in Finite Automata

DAIMI Report Series ◽

10.7146/dpb.v6i82.6498 ◽

1977 ◽

Vol 6 (82) ◽

Author(s):

Erik Meineche Schmidt

Keyword(s):

Regular Expression ◽

Finite Automata ◽

Regular Languages ◽

Deterministic Finite Automata

<p>The gain in succinctness of descriptions of regular languages when nondeterministic (unambiguous) finite automata are used rather than unambiguous (deterministic) finite automata, is not bounded by any polynomium.</p><p>The problem of deciding whether an unambiguous regular expression does not generate all words over its terminal alphabet, is in NP.</p>

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State Complexity of k-Union and k-Intersection for Prefix-Free Regular Languages

International Journal of Foundations of Computer Science ◽

10.1142/s0129054115500124 ◽

2015 ◽

Vol 26 (02) ◽

pp. 211-227 ◽

Cited By ~ 1

Author(s):

Hae-Sung Eom ◽

Yo-Sub Han ◽

Kai Salomaa

Keyword(s):

Lower Bound ◽

Upper Bound ◽

Finite Automata ◽

Constant Factor ◽

The State ◽

Regular Languages ◽

Deterministic Finite Automata ◽

State Complexity ◽

Binary Alphabet ◽

Multiple Intersections

We investigate the state complexity of multiple unions and of multiple intersections for prefix-free regular languages. Prefix-free deterministic finite automata have their own unique structural properties that are crucial for obtaining state complexity upper bounds that are improved from those for general regular languages. We present a tight lower bound construction for k-union using an alphabet of size k + 1 and for k-intersection using a binary alphabet. We prove that the state complexity upper bound for k-union cannot be reached by languages over an alphabet with less than k symbols. We also give a lower bound construction for k-union using a binary alphabet that is within a constant factor of the upper bound.

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DESCRIPTIONAL COMPLEXITY OF NFA OF DIFFERENT AMBIGUITY

International Journal of Foundations of Computer Science ◽

10.1142/s0129054105003418 ◽

2005 ◽

Vol 16 (05) ◽

pp. 975-984 ◽

Cited By ~ 36

Author(s):

HING LEUNG

Keyword(s):

Finite Automata ◽

Regular Languages ◽

The Other ◽

Deterministic Finite Automata ◽

Descriptional Complexity ◽

Nondeterministic Finite Automata ◽

Initial States

In this paper, we study the tradeoffs in descriptional complexity of NFA (nondeterministic finite automata) of various amounts of ambiguity. We say that two classes of NFA are separated if one class can be exponentially more succinct in descriptional sizes than the other. New results are given for separating DFA (deterministic finite automata) from UFA (unambiguous finite automata), UFA from MDFA (DFA with multiple initial states) and UFA from FNA (finitely ambiguous NFA). We present a family of regular languages that we conjecture to be a good candidate for separating FNA from LNA (linearly ambiguous NFA).

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A polynomial double reversal minimization algorithm for deterministic finite automata

Theoretical Computer Science ◽

10.1016/j.tcs.2013.03.005 ◽

2013 ◽

Vol 487 ◽

pp. 17-22 ◽

Cited By ~ 6

Author(s):

Manuel Vázquez de Parga ◽

Pedro García ◽

Damián López

Keyword(s):

Finite Automata ◽

Minimization Algorithm ◽

Deterministic Finite Automata

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

International Journal of Foundations of Computer Science ◽

10.1142/s0129054120420071 ◽

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.

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COMPLEXITY IN UNION-FREE REGULAR LANGUAGES

International Journal of Foundations of Computer Science ◽

10.1142/s0129054111008933 ◽

2011 ◽

Vol 22 (07) ◽

pp. 1639-1653 ◽

Cited By ~ 18

Author(s):

GALINA JIRÁSKOVÁ ◽

TOMÁŠ MASOPUST

Keyword(s):

Free Path ◽

Finite Automata ◽

Regular Languages ◽

Regular Expressions ◽

Deterministic Finite Automata ◽

Union Operation

We continue the investigation of union-free regular languages that are described by regular expressions without the union operation. We also define deterministic union-free languages as languages accepted by one-cycle-free-path deterministic finite automata, and show that they are properly included in the class of union-free languages. We prove that (deterministic) union-freeness of languages does not accelerate regular operations, except for the reversal in the nondeterministic case.

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