Questions tagged [fl.formal-languages]

formal languages, grammars, automata theory

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Different definitions of grammar complexity

It's known that there are different "kinds" of grammar complexity of language $L$ --- nonterminal complexity (minimal possible $|N|$ for grammar $(N, \Sigma, P, S)$ generating $L$), covering ...
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1answer
78 views

Nonterminal descriptional complexity of regular languages

Recently I became interested in grammar complexity of regular language. Prior to searching for literature, I tried to investigate it on my own, proving two lemmas from comment below. I am aware of an ...
8
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95 views

Deciding whether DCFG is visibly pushdown

Is the following problem decidable? If so, what's the best algorithm known? Instance: a deterministic pushdown automaton $A$ Question: Does there exist (i) some partition of the alphabet into push, ...
3
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1answer
120 views

how to define “correlation” between languages?

How does one define the concept of correlation between languages? Is there any 'standard' measure of 'correlation' between two (possibly inf) sets of strings / an analogue of the concept in this ...
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162 views

Regular languages accepted by an automaton with at most one transition per letter

I'm interested in the (very restricted) subset of regular languages for which there is an automaton having the following property: for every letter $a$ of the alphabet, the automaton has at most one ...
3
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1answer
92 views

Generalizations of Dyck languages?

The "narrowest" generalization of Dyck languages that I am aware of is Visibly Pushdown languages. Are there any useful classes of languages that are intermediate between Dyck languages and ...
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1answer
135 views

What graphs on $\mathbb{N}$ can be encoded as regular languages?

Suppose I represent the natural number 0 by "x", and use the symbol "s" for successor so that I get the following encoding of $\alpha : \mathbb{N} \rightarrow V$ of natural numbers ...
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23 views

Decidability of regular partition construction given its existence

Let $G = (N,T,P,S)$ be a context-free grammar where $T,N$ are sets of terminals and nonterminals respectively, $P$ contains all the productions of the grammar, and $S \in N$. If we know that $G$ is LL(...
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0answers
15 views

Power of Hyperedge Replacement Grammars (HRGs)

Can HRGs generate languages which equal or include the following graph languages: All (bipartite) graphs of bounded degree All (bipartite) planar graphs of bounded degree All (bipartite) planar ...
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3answers
277 views

Why do people bring real-life Quantum Computing to the discussion of the Church-Turing thesis?

As an undergraduate with limited understanding of QC and even the C-T thesis, I have problems figuring out why in questions such as Extended Church-Turing Thesis real-life quantum stuff is even given ...
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1answer
79 views

How to prove that Supremum preorder coincides with Hoare preorder?

Given a complete lattice $(L, \sqsubseteq)$ and a basis of completely $\sqcup$-irreducibles $B_L \subseteq L$, such that $\forall l \in L$, $l=\sqcup\{b \in B_L\ |\ b \sqsubseteq l\}$. I mean: Hoare ...
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1answer
145 views

Kolmogorov Complexity of a Decidable Language

The Kolmogorov Complexity (KC) of a string $y$ is the size of the smallest program $f$ and input $x$ that: $y = f(x)$. Let's define a variation of Kolmogorov's complexity$^1$. Suppose a decidable ...
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2answers
246 views

2DFA to 1DFA - Converting two way deterministic finite automata to one way deterministic finite automata

How can I convert a 2DFA to a normal DFA. Is there an algorithm/elegant way to do that ? I've been researching this for a few days but I coundn't find anything. Actually I want to implement that in ...
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0answers
118 views

Languages whose Parikh image is recognizable

Let $\Sigma$ be some alphabet, and $p : \Sigma^* \to \mathbb N_0^{|\Sigma|}$ the Parikh map. A formal language $L \subseteq \Sigma^*$ is called a slip-language, if $p(L)$ is a semilinear set. By ...
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Proof: Why are MM-1QFA strictly more powerful than MO-1QFA? // Quantum automata

While dealing with quantum finite automata (QFA), I repeatedly come across the statement that measure-many QFA (MM-1QFA, KW97) are strictly more powerful than measure-once QFA (MO-1QFA, MC97). More ...
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5answers
547 views

NP-complete decision problems on deterministic automata

Do you know any NP-complete decision problems on deterministic automata? Most NP-complete problems that come to my mind are either (see, or here) graph theoretical, or involve some string rewriting or ...
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32 views

Name for family of language classes closed under union, inverse gsm mapping and intersection with regular

Is there a name for language classes closed under union, inverse gsm mappings and intersection with regular languages? This is a bit similar to trio or AFL, but I specifically do not want to require ...
3
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1answer
102 views

Embarrassingly Parallel: Formal Definition & Citation

I've been unable to find a good answer for this question: Formally, what makes a problem embarrassingly parallel? Intuitively, it would seem to me that an embarrassingly parallel problem is one where: ...
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3answers
546 views

Maximum shortest word accepted by pushdown automata

Given a fixed alphabet, consider all deterministic pushdown automata with $n$ states that accept a nonempty language. What is the maximum length of the shortest word accepted by a deterministic ...
3
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0answers
85 views

The number of words of length $n$ in a context-sensitive language

Let $L$ be a context-sensitive language, $s_{L}(n)$ is denoted by the number of words of length $n$ in $L$. What is known about $s_{L}(n)$? Note that it is known that $s_{L}(n)$ is either polynomial,...
3
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1answer
101 views

Term for a set that is not immune

At the outer bounds of computational complexity classes are those defined through computability theory (AKA recursion theory). This is where we get the well known complexity classes such as R, RE, and ...
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2answers
168 views

Is the decidability of a language decidable? [closed]

Is there a Turing machine that takes a language as input and decides/semi-decides if it is a decidable language? Comments + answer say trivially the answer is yes; however, I'm wondering here would ...
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3answers
363 views

what is a model of computation, mathematically? [closed]

Where can I find a mathematical definition for "model of computation"? https://en.m.wikipedia.org/wiki/Model_of_computation doesn't provide a precise definition for "model of computation"--it doesn't ...
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0answers
48 views

Incompleteness and term extraction

Is there a formalization, which from a proof that a system includes enough arithmetic extracts an arithmetic sentence in the language of PA, which is not provable in the given system? Imagine the ...
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1answer
63 views

Chomsky-Schutzenberg Hierarchies explained for physicist (general) [closed]

I am classically trained in physics, however I have been interested in the use of information theory in studying some classical systems. As someone who is somewhat unfamiliar with the language of ...
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1answer
105 views

Ordered Grammar in THEORY OF COMPUTATION [closed]

What is ordered grammar in the theory of computation?
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1answer
282 views

What class of languages is recognized by finite-state automata with $k$ heads?

A DFA or NFA reads through an input string with a single head, moving left-to-right. It seems natural to wonder about finite-state machines that have multiple heads, each of which moves through the ...
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1answer
135 views

How are safety/liveness languages defined on the set of finite or infinite words?

Let $Σ$ be an alphabet (e.g., the powerset of atomic propositions coming from some Kripke structure, though such details are irrelevant here). For infinite words, a language $P\subseteq Σ^ω$ is ...
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1answer
127 views

Gödel-Numbering of the Context-Sensitive Languages

I would like to have a Gödel-numbering of the context-sensitive languages. Because there is no obvious syntactic distinction between LBAs and TMs, I cannot number the former in an immediate way. So I ...
5
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1answer
108 views

k-testable languages with non-constant k?

Let $p_t(w)$ and $s_t(w)$ denote the prefix and suffix of length $t$ of the word $w$, respectively. If $|w| < t$, then $p_t(w) = s_t(w) = w$. Furthermore, let $i_t(w)$ be the set of infixes of ...
3
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0answers
45 views

Extending the sequential calculus (logic over words) to allow a hierarchy of languages like the arithmetical hierarchy

Let $\Sigma$ be some finite alphabet. Then consider the logical language $\mathcal L = \{ R_a : a \in \Sigma \} \cup \{ <,= \}$ and first order formulas. For a given first order formula $\varphi$ a ...
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0answers
104 views

Notion of “quotient” or “inverse” for recognizable tree languages?

Related to my previous question but this time I have a better idea of what I'm actually asking. I'm looking at the following operation on recognizable tree languages (i.e. regular tree grammars, ...
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0answers
56 views

Regular Tree Languages are closed under quotient?

The Wikipedia page for Regular Tree Grammars notes that if $L_1$ and $L_2$ are regular tree languages, than $L_1 \setminus L_2$ is as well. However, it doesn't define this quotient operation for trees,...
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1answer
292 views

Is the Set of all Primitive Words a Prime Language?

A word $w$ is called primitive, if there is no word $v$ and $k > 1$ so that $w = v^k$. The set $Q$ of all primitive words over an alphabet $\Sigma$ is a well known language. WLOG we can choose $\...
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1answer
170 views

A conjecture related to the Cerny conjecture - counterexample/reference request

The Cerny conjecture is the statement that any synchronizing automaton with $n$ states has a synchronizing word of length at most $(n-1)^2$. The best current upper bound for the length of a ...
6
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1answer
166 views

Arranging letters to make a word in a regular language

Fix a regular language $L$ on the alphabet $\{a, b\}$, and consider the following problem. I am given as input: some number $m \in \mathbb{N}$ of copies of the letter $a$, and some number $n \in \...
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42 views

Is there an unambiguous grammar that has no left recursion or left factors, but is not in $LL(1)$?

I know that, for a grammar $G$ to belong to $LL(1)$, it is necessary that $G$ is not ambiguous; that is, every sentence has a unique parse tree in $G$. $G$ has no left recursion; that is, we can't ...
13
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1answer
264 views

Is { ww' | HamDist(w,w')>1 } context-free?

After reading the recent question "Is the complement of $\{ www \mid ...\}$ context-free?"; I remembered a similar problem I wasn't able to disprove: Is $L = \{ ww' \mid w,w' \in \{0,1\}^* \land |w|...
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3answers
437 views

Continuous mathematics and formal language theory

Whether there are some results on solving formal languages problems using mathematical analysis, continuous mathematics. For example, solving the intersection non-emptiness problem for a context-free ...
5
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1answer
165 views

For which $R$ is $\{0^a10^b10^c\mid R(a,b,c)\}$ context-free?

Unless I'm mistaken, a language of the form $\{0^a10^b\mid R(a,b)\}$ is context-free if and only if $R$ is a finite union of linear (in)equalities involving integer constants and the variables $a$ and ...
12
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3answers
421 views

Is the complement of { www | … } context-free?

It is well-known that the complement of $\{ ww \mid w\in \Sigma^*\}$ is context-free. But what about the complement of $\{ www \mid w\in \Sigma^*\}$?
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1answer
264 views

Size of complement of context-free language

Let $L$ be a context-free language, $\bar L$ be its complement and $\bar L_n$ be the length $n$ words in $\bar L_n$. What is known about $|\bar L_n|$? Note that it is known that $|L_n|$ is either ...
0
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1answer
92 views

Why can't a left-recursive, non-deterministic, or ambiguous grammar be LL(1)?

I've learned from several sources that an LL(1) grammar is: unambiguous, not left-recursive, and, deterministic (left-factorized). What I can't fully understand is why the above is true for any LL(1)...
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2answers
443 views

Does a given regular language contain an infinite prefix-free subset?

A set of words over a finite alphabet is prefix-free if there are no two distinct words where one is a prefix of the other. The question is: What is the complexity of checking whether a regular ...
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0answers
117 views

Are there cascade decompositions of machines that are more general than finite automata?

The idea of decomposing automata and their associated semi-groups into irreducible sub-components is due to Krohn & Rhodes and has been explored relatively thoroughly. Krohn & Rhodes gave an ...
9
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1answer
109 views

Is there a method for proving non-regularity of string transformations?

There are a number of different models for defining transformations between languages. Finite state transducers and MSO-definable graph transformations over string graphs are the two that I am best ...
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1answer
1k views

Number of words of length n in a context-free language

Denote by $w_n$ the number of words of length $n$ in a (possibly ambiguous) context-free language. What is known about $w_n$? I'm sure this has been studied a lot, but I couldn't find anything at ...
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4answers
584 views

Base-k representations of the co-domain of a polynomial - is it context-free?

In chapter 4 of Jeffrey Shallit's A Second Course in Automata Theory the following problem is listed as open: Let $p(n)$ be a polynomial with rational coefficients such that $p(n) \in \mathbb{N}$ for ...
7
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0answers
83 views

Reference request: transforming a grammar to Greibach normal form preserves the number of parse trees

I believe that most "natural" ways of transforming a grammar to the GNF should preserve the number of parse trees for each string. For example, Urbanek's construction from the paper "On Greibach ...
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1answer
351 views

What is the practical importance of making or using a Turing complete language? [closed]

I get what a Turing machine is and what language is a Turing-complete language but when someone introduces me to a new programming language (like Solidity) and says it is Turing complete, what am I ...

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