formal languages, grammars, automata theory

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Is inclusion of DCFL (or even DCSL) decidable?

Given two deterministic context-free languages $L_1$ and $L_2$, is $L_1 \subset L_2$ decidable? If so, in what complexity class may such an algorithm be? It is clear that the same problem for ...
3
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1answer
82 views

Closure properties of deterministic context-sensitive languages

There does seem to be a lot of information regarding the closure properties of both deterministic context-free and nondeterministic context-sensitive languages. However, the literature is almost mute ...
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35 views

Complexity Classes (P, NP) vs Language Hierarchies (REC, RE) [migrated]

Is there any relation between the Complexity Classes (like P or NP) and Language hierarchies (like REC or RE) ? Form what I understand: (easy things are the things that can be done in polynomial ...
5
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2answers
85 views

Can real-time deterministic multicounter automata recognize the marked palindrome language?

Consider the marked palindrome language which is defined as MPAL=$\{ w\#w^r | w \in \{a,b\}^* \}$. It is easy to recognize MPAL using only a single stack. My question is whether MPAL can be ...
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0answers
97 views

Is there an algorithm to find whether 2 combinators form a Turing-complete system?

It is known that K = (λx.(λy.x)) and S = (λx.(λy.(λz.((x z) (y z))))) define a turing complete system, and we know procedures to ...
10
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1answer
309 views

Decide the existence of a string homomorphism

Consider the following problem: Given two strings x,y, decide whether there exists a string homomorphism f such that f(x)=y. It is easy to show that this problem is in $NP$. Are there other ...
14
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2answers
233 views

Does XOR automata (NXA) for finite languages benefit from cycles?

A non-deterministic Xor automata (NXA) is syntactically an NFA, but a word is said to be accepted by NXA if it has an odd number of accepting paths (instead of at least one accepting path in the NFA ...
4
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2answers
186 views

Bounds on size of self-concatenation of Finite Languages

Given a finite language $L$ with $|L|$ number of elements, what is $|L^i|$ (the language $L$ concatenated with itself $i$ times)? If there is no exact result, is there an upper/lower bound? Define ...
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0answers
70 views

What is the importance of linear languages?

What is the point of linear languages? They appear to be an intermediate set of languages in between regular and context-free languages, but do they have any useful or nice properties that either have ...
3
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0answers
114 views

Restricted-Input Automaton

In the classic setting, an automaton for a language $L$ is required to accept all words in $L$ and reject/get stuck on every word in $\Sigma^*\setminus L$. All of the related concepts are then ...
10
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186 views

Can we approximate the number of words accepted by an NFA?

Let $M$ be an acyclic NFA. Since $M$ is acyclic, $L(M)$ is finite. In a related question, it was suggested that exact counting of the number of words accepted by $M$ is $\#P$-Complete. The second ...
5
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1answer
133 views

What language $L \in NCM$ has $\overline{L} \not \in NCM$?

$NCM$, the class of non-deterministic reversal-bounded counter machines, has a lot of interesting dependability and closure properties. It's known that, unlike the deterministic version, NCM is not ...
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1answer
146 views

Bounds on the size of NFA for $r$-skip $k$-distinct language

This question is about an extension of a language discussed in this question. We define the $r$-skip $k$-distinct language as follows: $$L_{r,k}=\{\sigma_1\sigma_2\cdots \sigma_{rk}\in\Sigma^{rk} | ...
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0answers
74 views

In what complexity classes other than $NP$ are these problems related to unary languages?

If I remember correctly saw this reduction in a paper can't find at the moment. Consider the following NP-complete variation of the Subset Sum problem. Given a set of positive integers ...
4
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1answer
204 views

What characterizations exist for the grammars that can express subsets of the context-free languages?

It is well known that CFGs and PDAs are equivalent, and there has been extensive research about the relationship between deterministic pushdowns and $LR(1)$ grammars, as $DCFL$ is a subset of $LR(1)$. ...
6
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2answers
115 views

Are deterministic context-free languages closed under outfix (or other erasing operations)

Define the outfix of a language $L$ to be $Outf(L) = \{xy \mid \exists z. xzy \in L \}$. Are any known results about whether deterministic context-free languages are closed under this operation, or ...
20
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3answers
208 views

Complexity of intersection of regular languages as context-free grammars

Given regular expressions $R_1, \dots, R_n$, are there any non-trivial bounds on the size of the smallest context-free grammar for $R_1 \cap \cdots \cap R_n$?
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1answer
178 views

Natural examples of context-sensitive languages from practice

I am looking for natural examples of context-sensitive languages from practice. For example, reasonable answers could include grammar syntax of a programming language, or encoding of certain ...
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0answers
58 views

Can the definition of ambiguity of CFG be extended to CSG?

Usually,ambiguity of grammar is defined for constext-free languages and grammars,sometime it is extended to indexed languages and grammar,but the extension of definition of the definition is same ...
13
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4answers
347 views

What notable automaton models have polynomially-decidable containment?

I'm trying to solve a particular problem, and I thought I might be able to solve it using automata theory. I'm wondering, what models of automata have containment decidable in polynomial time? i.e. if ...
15
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1answer
362 views

Can constant ambiguity reduce the state complexity of a regular languages?

We say that NFA $M$ is Constantly Ambiguous if there exist $k\in \mathbb{N}$ such that any word $w\in \Sigma^*$ is accepted by either $0$ or (exactly) $k$ paths. If automaton $M$ is constantly ...
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1answer
127 views

Asymptotic density of ambiguous context-free grammars (CFGs)

What is the ratio of ambiguous CFGs to all CFGs? Since both sets are countably infinite the ratio is not well-defined. But what about the asymptotic density: $$\lim_{n \mapsto \infty}\frac {\# ...
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2answers
71 views

Looking for menu-driven coding editor based on a programming language state machine [closed]

I'd like to know whether an application development environment exists that uses a menu-driven coding editor that employs a programming language state machine. This would mean that commands, variable ...
4
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1answer
217 views

What are the relationship and difference between ambiguous grammars and non-deterministic ones?

Intuitively, I had assumed that ambiguous grammars were roughly the same as non-deterministic grammars. According to Wikipedia however, this is false: there are non-deterministic unambiguous CFGs ...
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0answers
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Which paper first showed that any context-free grammar (CFG) is equivalent to some CFG in Chomsky normal form?

Which paper first showed that any context-free grammar (CFG) is equivalent to some CFG in Chomsky normal form? I cannot find an reference.
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1answer
274 views

Languages recognized by polynomial-size DFAs

For a fixed finite alphabet $\Sigma$, a formal language $L$ over $\Sigma$ is regular if there exists a deterministic finite automaton (DFA) over $\Sigma$ which accepts exactly $L$. I am interested in ...
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0answers
53 views

An algorithm for extracting grammars given existing grammar

Let all the grammars of concern here be CFGs. Let $A$ be a grammar with rules $A^i \Rightarrow a_1^i \dots a_{n_i}^i, \ i = 1 \dots n$, where each $a_i^j$ is either a terminal in $\Sigma$ or a rule ...
8
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1answer
216 views

Reversible Turing tarpits?

This question is about whether there are there any known reversible Turing tarpits, where "reversible" means in the sense of Axelsen and Glück, and "tarpit" is a much more informal concept (and might ...
8
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1answer
267 views

Lower bound for NFA accepting 3 letter language

Related to a recent question (Bounds on the size of the smallest NFA for L_k-distinct) Noam Nisan asked for a method to give a better lower bound for the size of an NFA than what we get from ...
4
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3answers
190 views

Regular languages under change of encoding

Consider a regular language $L$ with alphabet $\Sigma = \{0,1\}$. Can we say that the set of strings in $L$ (representing non-negative integers in binary encoding) when represented in some other ...
12
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2answers
188 views

Reference for Dyck languages being $\mathsf{TC}_0$-complete

Dyck languages $\mathsf{Dyck}(k)$ is defined by the following grammar $$ S \rightarrow SS \,|\, (_1 S )_1 \,|\, \ldots \,|\, (_k S )_k \,|\, \epsilon $$ over the set of symbols ...
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2answers
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Tool for specifying operational semantics for given formally specified programming language

I am trying to translate code from one programming language into another (to be specific - from RuleML to Drools, but other pairs can be expected as well) and it would be nice to know - whether there ...
11
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2answers
305 views

Why is linearizability a safety property and why are safety properties closed sets?

In Chapter 13 "Atomic Objects" of the book "Distributed Algorithms" by Nancy Lynch, linearizability (also known as atomicity) is proved to be a safety property. That is to say, its corresponding trace ...
4
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2answers
148 views

Higher order Quines - when do super Quines exist?

The normal Quine - a program that prints its own code - is a special case of an n-Quine. An n-Quine is a program that prints code for a different program that after n iterations of printing and ...
16
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0answers
180 views

Is there a regular tree language in which the average height of a tree of size $n$ is neither $\Theta(n)$ nor $\Theta(\sqrt{n})$?

We define a regular tree language as in the book TATA: It is the set of trees accepted by a non-deterministic finite tree automaton (Chapter 1) or, equivalently, the set of trees generated by a ...
10
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2answers
202 views

The number of states of local automata

A deterministic automaton $\mathcal A = (X, Q, q_0, F, \delta)$ is called $k$-local for $k > 0$ if for every $w \in X^k$ the set $\{ \delta(q,w) : q \in Q \}$ contains at most one element. ...
11
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2answers
322 views

How small can a NFA be, compared to the minimal Unambiguous Finite Automaton (UFA) of the same regular language?

Unambiguous Finite Automatons (UFA) are special type of non-deterministic finite automatons (NFA). A NFA is called $unambiguous$ if every word $w\in \Sigma^*$ has at most one accepting path. This ...
4
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1answer
64 views

The polynomial languages and ordered syntactic monoids

A polynomial language is a languge which could be represented as the finite union of languages of the form: $$ A_0^* a_1 A_1^* a_2 \cdots a_k A_k^* \quad a_i \in X, A_i \subseteq X $$ Such an ...
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1answer
146 views

Computing the Syntactic Congruence

The syntactic monoid of a language $L \subseteq X^*$ is defined as the monoid obtained from the congruence relation $$ u\ \tilde{}\ v \ \mbox{ iff }\ \forall x,y \in X^* : xuy \in L \leftrightarrow ...
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0answers
90 views

Deciding whether a binary multiplicity automaton has empty language

Multiplicity automatons (see here) is an interesting model. They have the (almost) same syntax as a non-deterministic finite automatons, but instead of deciding whether a word belongs to a language, ...
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1answer
108 views

Adherence of languages and the Dyck language

Let $L \subseteq X^*$ and $X = \{a,b\}$ be a language of finite words, denote by $A(u)$ the prefixes of some word (finite or infinite), then the adherence $\mbox{Adh}(L)$ is defined to be the set of ...
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1answer
64 views

Assessing complexity of a language using subset relations

What makes a language hard in a computational sense is neither simply that it contains very few words(e.g. is finite) or that it contains a lot of words(e.g. is infinte) but rather an intricate ...
3
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0answers
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Transfering properties from subsets of $X^*$ to subsets of $X^{\omega}$ by using the topology induces by Cantor space

A language $L \subseteq X^*$ is non-counting of order $n > 0$ iff for all $u,v, w \in X^*$ $$ uv^nw \in L \Leftrightarrow uv^{n+1} w \in L. $$ A $\omega$-language (set of infinite sequences) $L ...
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1answer
67 views

Difference between locally testable and it's boolean closure

A language $L$ is called i) locally testable in the strict sense iff there exists $P, S, I \subseteq X^*$ such that $$ w \in L \mbox{ iff } pref^k(w) \in P, suffix^k(w) \in S, infix^k(w) \subseteq ...
14
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1answer
243 views

Can a two counters machine decide $n^2$?

Can a standard two counters ($c_1,c_2$) machine with the following instructions: ...
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0answers
86 views

Subsets of $\omega$-words which share certain factors and languages accepted by special (prefix-closed) automata

Let $\mathcal A$ be an automaton, then I define the following $\omega$-language accepted by $\mathcal A$: $$ L'(\mathcal A) := \{ \eta \in X^{\omega} : v \sqsubset \eta \mbox{ implies } v \in ...
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4answers
232 views

Questions about regular languages and their sublanguages

I am interested in the following questions and would be grateful if anyone could give me hints or point me to articles: 1) Given a regular language $L$, what are its regular sublanguages $L'\subseteq ...
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2answers
196 views

Smallest Boolean circuit to generate a language

Consider a non-empty language $L$ of binary strings of length $n$. I can describe $L$ with a Boolean circuit $C$ with $n$ inputs and one output such that $C(w)$ is true iff $w \in L$: this is ...
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1answer
108 views

Does every regular language contains a strictly locally testable language?

Let $L$ be an infinite regular language, then does there exists a strictly locally testable infinite language $P$ such that $P \subseteq L$?
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78 views

Formal languages induced by ultrafilters

Let $I$ be the set of all recursively enumerable languages over an alphabet $\Sigma$. Let $$S_\alpha=\{i\in I : \alpha\in i\}$$ for all $\alpha\in\Sigma^*$. Then $$E=\{S_\alpha:\alpha\in ...