Automata Theory, including abstract machines, grammars, parsing, grammatical inference, transducers, and finite-state techniques

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Question about a possible notion of ordinal machine

Let $S$ be a set of ordinals. By a parametric functor, we mean a pair $(F,G)$ where $F : S \rightarrow S$ is an ordinal functor, and $G$ is a map which takes a function $f : S \rightarrow S$, two ...
0
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0answers
35 views

Proving a language (ir)regular (standard methods have failed) [migrated]

I'm currently trying to prove a language regular (for personal amusement). The language is: The language containing all numbers in ternary that have even bit-parity when encoded in binary. Now, I've ...
9
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1answer
227 views

Are there non-constructive proofs of existence of “small” Turing machines / NFAs?

After reading a related question, about non-constructive existence proofs of algorithms, I was wondering if there are methods of showing existence of "small" (say, state-wise) computation machines ...
1
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0answers
63 views

Relations between Arboreal Group Theory and Tree Group Actions? [migrated]

By a tree group action, we mean an action of a group $G$ over the infinite regular binary tree $T_2$ such that for each $g \in G$, the mapping $x \rightarrow g.x$ is an automorphism of $T_2$; these ...
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12 views

Help me resolve my doubts about infinities, exemlified by an example of non DFA acceptable language [migrated]

I have always had a hard time making sense of infinities. Example: the language $L = \{ \epsilon , 01, 0011, 000111, 00001111, ... \}$ is not DFA acceptable because a machine capable of ...
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1answer
69 views

is determining an unknown CFL from intersection of two CFLs decidable?

this problem was asked over a week ago on cs.se now with 7v and no answers so far, ie still "open". (there are many somewhat related problems/near variants re CFLs but its not obvious how to reduce it ...
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0answers
32 views

DNA to organism model for software

This question is not about DNA computing. I have tried searching for a software or algorithm design/model which works like an organism. I mean, almost every organism starts its life from DNA and ...
8
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1answer
171 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 ...
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1answer
186 views

Theta functions of automata relations

Let $A,B$ be two automata over the same alphabet $\Sigma$; they are supposed to be complete, strongly connected DFAs. We denote by $._A$ (resp. $._B$) the action induced by $\Sigma^*$ over $Q(A)$, ...
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3answers
125 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 ...
5
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0answers
123 views

Data structures for Finite Automata

I am a Control Engineer and I have been working on Discrete Event Systems and Supervisory Control, based on Finite Automata Theory. My problem is to represent large automata (about $2 \times 10^6$ ...
6
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63 views

Conjecture about two counters automata

I would like to prove (or disprove) the following conjecture: Conjecture: a two counter automata (2CA) cannot decide the following language: $L = \{ n \mid $ the ternary and binary representations ...
7
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2answers
122 views

A tool for minimal NFA computation

It is well known that minimizing an NFA for a fixed regular language is $PSPACE-Complete$. As far as I know, there are no better than trivial algorithms for minimizing such NFA, but there's a little ...
1
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1answer
51 views

On equivalence of NLBA and DLBA

Where I can find reference and documents on the work made for proving whether DLBA are equal NLBA nr not? What is the underlying problem? Why it is still an open question in TCS?
1
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1answer
203 views

What are good conferences for algorithms about finite automata?

I am writing a research paper, which describes some properties about finite automata. It also provides a couple of algorithms that can measure some aspects of the properties. Could you point out some ...
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2answers
218 views

Difference between infinite state machines and turing machines

Finite state machines (FSM) are strictly less powerful than turing machines (TM). But this is not the case with infinite state machines (ISM). For example, every TM can be embedded into some ISM. ...
3
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0answers
90 views

Concentration of Stationary Distribution on Random Directed Graphs

We consider a random directed graph with fixed out-degree $d$. Each vertex chooses $d$ neighbors with replacement, uniformly and independently. Self-loops and multiple arcs are allowed in this model. ...
8
votes
2answers
148 views

The number of states of local automata

A deterministic automata $\mathcal A = (X, Q, q_0, F, \delta)$ 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. ...
2
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0answers
60 views

WFSA over hyperreals

Are there any works where authors tried to define weighted finite state automata over hyperreals (or a similar object allowing for infinite and infinitesimal values) in an attempt to make automata ...
10
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2answers
263 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
51 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 ...
5
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1answer
89 views

Inverse of transducer compositions

Consider a Generalized Sequential Machine (GSM; or nearly equivalently -- an FSM transducer). These machines are closed under compositions. A composition of two GSMs $f(x)$ and $g(x)$ can be written ...
2
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1answer
105 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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73 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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2answers
500 views

Bounds on the size of the smallest NFA for L_k-distinct

Consider the language $L_{k-distinct}$ consisting of all $k$-letter strings over $\Sigma$ such that no two letters are equal: $$ L_{k-distinct} :=\{w = \sigma_1\sigma_2...\sigma_k \mid \forall ...
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1answer
74 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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62 views

Sub optimal regex equivalence

Regex Equivalence is a hard problem which in general takes exponential space and exponential time. Are there any approximation/sub-optimal algorithms with some theoretical guarantees over equivalence ...
6
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0answers
162 views

Generalized sequential machine synthesis subject to language equivalence/inclusion and reachability

A generalized sequential machine (GSM) is a generalization of a Mealy machine where on each transition one input symbol is read and 0 or more output symbols are written. As in a Mealy machine, we ...
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1answer
111 views

Intersection between context-free and context-sensitive language decidability [closed]

I'm trying to find a formal proof of the following fact: Given a context-free language, say $L_1$, and a context-sensitive language, say $L_2$, it is NOT decidable if their intersection is empty ...
8
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2answers
155 views

2DFA that requires many states in equivalent DFA?

Is there a 2DFA with $n$ states (where $n$ is nontrivial, say at least 4) that requires at least $2^n$ states to simulate using any DFA? A two-way DFA (2DFA) is a deterministic finite-state ...
3
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0answers
84 views

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 ...
0
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1answer
63 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 ...
3
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0answers
84 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
205 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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1answer
104 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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128 views

Finding self-similar homomorphisms of a FSM transducer

Consider a special case of homomorphisms of FSM transducers (or "generalized sequential machines" in [1]). Let $F$ be a transducer accepting a language $L$, and let $h(x)$ be a homomorphism function ...
9
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153 views

Minimizing residual finite state automata

Residual finite state automata (RFSAs, defined in [DLT02]) are NFAs that have some nice features in common with DFAs. In particular, there is always a canonical minimum sized RFSA for every regular ...
4
votes
1answer
84 views

When does a set of infixes determine a set of ($\omega$-) words

If a have a set of finite infixes of a specific length, which $\omega$-languages are determined by them, and furthermore, when does a set of infixes determine a $\omega$-word uniquely. For example for ...
2
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1answer
116 views

Closure Properties of Locally Testable Language

Are locally testable languages closed under complementation? I guess yes, because when I can decide membership by sliding a window of size $k$ over the word and looking if the $k$-length words ...
10
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1answer
158 views

Can one-way alternating automata with one-counter recognize some unary non-regular languages?

One-way alternating pushdown automata (1APDA) can recognize any language in $ DTIME(2^{O(n)}) $ (Alternation by Chandra, Kozen, and Stockmeyer, 1981). By replacing a pushdown storage of a 1APDA with a ...
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0answers
87 views

Properties of the number of copies of an NFA in each state

For an NFA $A$ with $n$ states and a word $w$, we can associate an $n$-dimensional vector $v_w$ with entries in $\mathbb{N}\cup\{0\}$ denoting the number of copies of the NFA in each state after ...
4
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3answers
174 views

How to minimize a FSM transducer?

In contrast to FSM minimization which is well studied with various algorithms, theorems and has many practical applications, I'm looking for any nontrivial insight, analysis and references to the ...
1
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0answers
87 views

Learning about Nested Stack Automata

I want to learn about nested stack automata. However my efforts to find a suitable learning resource have so far been abortive: The Wikipedia article on nested stack automata is a stub. Alfred Aho's ...
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votes
1answer
193 views

Can I show algebraically that this regular expression accepts all binary strings?

The task is to prove that (0+1)* and 0*(1.0*)* are equivalent. 1. http://rubular.com/r/K9Hp9tU6px 2. http://rubular.com/r/N8VpoEcch4 EDIT: Forgot that + was ambiguous here! I want to prove that the ...
5
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0answers
102 views

Has a result of Book and Greibach on Quasi-Realtime languages been improved?

Quasi-realtime languages are defined as languages accepted by nondeterministic multitape Turing machines in quasi-real time. Ronald Book and Sheila Greibach have shown in their 1970 paper that every ...
7
votes
3answers
229 views

Algorithm for ranking members of a regular language?

A little while back, I was reading a paper that mentioned a method for computing an integer 'rank' for a particular string $s \in L$ where $L$ is some regular language. This rank uniquely determines ...
7
votes
1answer
160 views

Measurability of an $\omega$-regular language

It the previous question of mine I put a reference which shows that any $\omega$-regular language over the alphabet $\Sigma$ is a Borel subset of $\Sigma^\omega$. I am not sure whether the reference I ...
6
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0answers
107 views

Separation of the states of a deterministic omega-automaton by looping words taken from a regular language of non-empty words

Consider a deterministic transition structure having states in set $X$ and transition function $\rightarrow$, and an initial state $x \in X$. This structure is intended to be part of an automaton ...
12
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211 views

Are there variants of visibly pushdown automata that allow pushing of words onto the stack?

I'm wondering, are there any papers or research dealing with visibly pushdown automata, but allowing words, rather than single letters, to be pushed onto the stack. Alternately, a construction which ...
6
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0answers
99 views

Are k+1 heads better than k for multiread finite automata?

Consider the deterministic (resp. non-deterministic) one-way finite automaton that is defined in the usual way except that it has k heads and in each step can decide which head to move. (It is allowed ...