Questions tagged [fl.formal-languages]

formal languages, grammars, automata theory

86 questions with no upvoted or accepted answers
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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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36 views

A class of languages admitted by a class of grammars equivalent to $\mathbf{PR}$?

Is there a class of languages $L(G)$ admitted by a class of phrase structure grammars $G$ equivalent to $\mathbf{PR}$? (the class of primitive recursive languages = $\mathbf{LOOP}$)? In greater ...
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82 views

Is there a DCSL that cannot be recognized in O(n^2) steps by a deterministic LBA?

Is there a context sensitive language $L$ so that $L$ cannot be recognized by a deterministic linear bounded turing machine in $O(n^2)$ steps, but still can be recognized by a deterministic LBA? The ...
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92 views

Proof of the equivalence of Muller automata and Parity (or Rabin chain) automata

Let $A$ be some finite alphabet and $\mathcal A = (Q, \delta, q_0)$ be some determinisitic finite automaton. Then $\mathcal A$ accepts infinite words $\xi \in A^{\omega}$ according to the Muller ...
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81 views

What is the class of the languages recognized by PCREs?

I have been considering building a tool that would convert regexes between the various syntaxes (BRE, ERE, PCRE). It is obvious that PCREs are too strong for the is-regular problem to be decidable, ...
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203 views

Complexity of DBA-recognizable Omega-Languages

Given an $\omega$-regular expression $r$, how difficult is it to decide if $L(r)$ is recognizable by some deterministic Büchi automaton? I know it is solvable in EXPTIME by converting the regular ...
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138 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 ...
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777 views

What is the relationship between the number of states in Quantum Finite Automata and the number of non-regular languages they can recognize?

It is has been shown that Quantum Finite Automata can recognize at least some non-regular languages. What is the relationship between the number of states in a qfa and the number of non-regular ...
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210 views

Fast weighted intersection algorithm for CFG and FSA with self loops but no other circles?

We all know that arbitrary CFG and FSA can be intersected using the Bar-Hillel Construction, whose time complexity is unfortunately too expensive. On the other hand, there are efficient algorithms ...
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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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44 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 ...
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62 views

Rational power series over $\mathbb N \cup \{\infty\}$, rationality of singular part

Let $\Sigma$ be a finite alphabet, and consider the formel power series over $\Sigma$ considered as non-commuting variables with coefficients in the semiring $\mathcal N := \mathbb N \cup \{\infty\}$ ...
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58 views

What is the interpretation of an infinite formal context-free grammar?

Let $L$ be a language as follows: $$ \begin{align*} L &::= a\ |\ L^{*}\\ \end{align*} $$ Now, suppose I apply some sort of transformation $T : N \rightarrow N$ where $N$ is the set of non-...
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33 views

Inductive definition of language operators like the set of all permutations of a word came from the shuffle operator

Let $X$ be a finite alphabet. Given two words $u, v \in X^{\ast}$ the shuffle operator is defined to be $$ u || v := \{ u_1 v_1 u_2 v_2 \ldots u_n v_n : 1 \le i \le n, u_i, v_i \in X^{\ast}, u = u_1 \...
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102 views

Possibly small circuit complexity class containing REG?

What is the smallest well-known Boolean-circuit complexity class containing all the regular languages over the binary alphabet {0,1}? If we believe Theorem 2 in Koucký, Circuit Complexity of ...
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78 views

What logic(s) exist for attributing belief?

I'm looking for an appropriate formalism to represent "traceability" in claims, especially connecting conclusions to source materials in a rigorous way. For example, I'd like to be able to represent ...
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41 views

Range concatenation grammars which are unambiguous as (and are NOT CFL)?

Are there any range concatenation grammars that generate only one possible parse tree are not also context-free?
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113 views

Relation between MDPs and non-deterministic finite automatons

I'm confused as to the relation (computability-wise) between markov decision processes and NFAs. Are finite state MDPs expressible as regular grammars? If so, are markov decision processes thus ...
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98 views

If for every non-terminal in a cs-grammar there exists an obligatory rule, does this alter the language of derivable strings

I am reading Chomsky's article Three models for the description of language, one of the earliest papers where context-free and context-sensitive grammars are mentioned. Essentially what he calls ...
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140 views

Why is an automaton on finite words co-deterministic iff its transitions are co-deterministic

In the article Automata and semigroups recognizing infinite words an automaton is specified by $\mathcal A = (Q, A, E, I, F)$ where $I$ is a set of initial states and $F$ a set of final states, $Q$ ...
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57 views

Grammars whose LR automata have singleton item sets?

The states in LR parsers correspond to sets of items (ie, sets of productions from the original grammar, with a "dot" marking how far into the rule the parser has gotten). In general, states ...
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86 views

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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98 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 K\subseteq\...
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39 views

Determine whether a categorical grammar is minimal concerning lexical entries

In order to compare the descriptional complexity of context-free and (combinatoric) categorical I need a way to check if a categorical grammar of a formal language is minimal concerning lexical ...
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92 views

Automatic structures/functions: Is (Z,+) under a unary representation automatic?

The group $(\mathbb{Z}, +)$ is automatic (ala Khoussainov) when using the "standard" representation in a decimal base. But if I want to use a different representation of Z, encoding my integers with ...
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191 views

Dynamic k-shortest paths in a weighted transducer

I'm looking for references relating to dynamically computing the k-shortest output paths through a stochastic, acyclic, weighted transducer that is being constructed on-the-fly. In this scenario ...
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643 views

Strategy for grammar derivation of a formal language

I wonder, whether there is any strategy/ies for grammar derivation of a formal language. I'd be thankful, if you give me some hints, tips on how should one "think" trying to find a grammar. I'm ...
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177 views

LALR grammars subsets

If LR(0) condition for a grammar G is formulated as follows: Every state is either reduction or a shift state and it can't be both at the same time if it is a reduction state, it contains exactly one ...
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181 views

Edit-Distance of weighted automata

I'm trying to understand "Edit Distance of Weighted Automata" by Mehryar Mohri: [83], [93] and [99] at http://www.cs.nyu.edu/~mohri/pub/ (they are virtually identical so which of them doesn't matter). ...
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313 views

Restricted read twice BDDs and context free grammars

Several papers give poly-time algorithms for constrained paths on labelled graphs, e.g. [1] Quote: Given an alphabet Σ, a (directed) graph G whose edges are weighted and Σ-labeled, and a formal ...
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13 views

Intuition on context free and other kinds of a forests? Data structures perspective

I am trying to gain intuition on formal forests, also called tree languages, i.e., sets of trees. There are regular tree languages, and there are context free tree languages. They both come in a ...
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49 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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160 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 ...
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159 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 $S=\{x_1,\...
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125 views

Given a sequence find the shortest reg exp that generates it?

I'm looking for a way to find the smallest possible regular-expression that accepts a sequence. To make it interesting I don't want any stars(Kleene stars) and preferably no wildcards? For instance ...
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176 views

Classification of Saturated LL(1) Grammars

By saturated I mean that the grammar accepts every possible string that can be constructed from the terminal set. So the parse table would be full of valid entries, no error entries at all. Can such a ...

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