All Questions
Tagged with formal-languages automata-theory
42 questions
2
votes
1
answer
124
views
Proof of dynamic programming calculation of Levenshtein distance
Let s1 and s2 are 2 arbitrary strings with lengths l1 and ...
- 203
3
votes
1
answer
807
views
Language equivalence between deterministic and non-deterministic counter net
One-Counter Nets (OCNs) are finite-state machines equipped with an integer counter that
cannot decrease below zero and cannot be explicitly tested for zero.
An OCN $A$ over alphabet $\sum$ accepts a ...
- 63
-3
votes
1
answer
531
views
Counter net decidability [closed]
Let one Deterministic Counter Net ($\mathrm{1DCN}$), which is a finite-state automata where every state is complete means all states has transition of all input symbols and their respective weight ...
- 63
2
votes
0
answers
64
views
A particular generalization of free partially commutative monoids
A trace monoid, or free partially commutative monoid, is one with the presentation $\langle \Sigma \mid a_1b_1 = b_1a_1, \dots, a_nb_n = b_na_n\rangle$. The theory of trace monoids has been well ...
- 21
4
votes
0
answers
170
views
Corollaries of Kleene's Theorem (Regular Languages)
Kleene's theorem that finite automata (specifically, nondeterministic) are expressively equivalent to regular expressions seems to be a powerful and not immediately obvious tool for untangling the ...
- 429
2
votes
0
answers
100
views
Name for the theory of words with equal length, prefix, successors
I've worked with this theory for a while, but I've never been quite sure what to call it:
$$(\Sigma^*, =_{el}, \preceq, (S_a)_{a \in \Sigma})$$
Where
$\Sigma^*$ is the set of finite words on finite ...
- 429
1
vote
1
answer
161
views
Errors in Waksman's Solution to Cellular Automaton Firing Squad Problem?
Recently, a student and I have been working through Waksman's paper ``An Optimum Solution to the Firing Squad Synchronization Problem.'' The paper claims that for any value of $n$, the proposed ...
- 413
2
votes
1
answer
70
views
For synchronizing eulerian finite state machines every proper subset of states has some larger state set leads to this subset
Suppose we have a deterministic complete finite automaton which is synchronized, meaning we have a reset word, i.e. a word which resets the automaton to a definite state, regardless from which state ...
- 798
1
vote
0
answers
265
views
What does homomorphism between languages mean to the correspoding Turing Machines?
According to the article: every c.e.language over $\Sigma^*$can be formed by homomorphism from a Dyck language over $\Sigma^{'}$ intersection with a minimal linear language over $\Sigma^{'}$ to the ...
- 3,084
5
votes
2
answers
545
views
Neighbourhood of a word and Levenshtein distance
The Levenshtein distance or Edit distance $$ lev(U,V) $$ between two strings $U$ and $V$ over a finite alphabet $\Sigma$ of size $ \left| \Sigma \right| = \sigma ,$ is the minimal number of insertions,...
- 61
-2
votes
1
answer
280
views
Deterministic Finite Automata question [closed]
I am very new to finite automata, and I came across an issue in my professors lecture slides which I think is wrong, and I'd wonder if any of you could confirm:
Alphabet: {1}
Automata
Surely the ...
- 7
2
votes
0
answers
47
views
Relation between indexed languages (OI-macro or context-free tree) and scattered context languages
I'm not sure about the relation between indexed languages (generated by indexed grammars--Aho) and scattered context languages (generated by
scattered context grammars--J Hopcroft).
I think that ...
- 21
1
vote
1
answer
260
views
The automorphism groups of smallest grammars of a language string are isomorphic
Let $s \in \Sigma^*$ be a formal language string. Consider the automorphism group of $s$, defined to be the set of all permutations of positions of $s$ that leave $s$ fixed. For instance $G(abab) = \...
- 260
1
vote
0
answers
58
views
Question about link between non-terminals of grammars and variables of Diophantine equations
If we change the right arrow in the rewriting rules of grammar into equators , changes all terminals into x and keep the non-terminals unchanged,we get system of equations.In some cases,those ...
- 3,084
6
votes
1
answer
165
views
Separating infinite words sharing factors by automata
Two infinite words $\xi, \eta \in X^{\omega}$ are separated by an (Büchi-)automaton if it accepts one but not the other.
Denote by $F_n(\xi)$ the factors of length $n$ of an infinite word $\xi$ and ...
- 798
6
votes
1
answer
135
views
Generalising the adherence operator and its closure properties with regard to regular (rational) languages
Let $X$ be an alphabet and denote by $X^{\omega}$ the set of all infinite sequences (i.e. words) in $X$. A subset $L \subseteq X^{\omega}$ is called $\omega$-regular if it is acceptable by some Büchi-...
- 798
2
votes
1
answer
143
views
Representability of sets of infinite sequences sharing common prefixes and factors (i.e. infixes)
Here we are concerned with the space $X^{\omega}$ of infinite sequences. Denote by $F_n(\xi)$
the set of factors (consecutive finite subsequences) of length $n$ and consider the set
$$
K_n(\xi) = \xi[...
- 798
0
votes
0
answers
154
views
Proof of conjecture that permutation-free automata restrict the possible states visitable from a stringset sharing prefixes and infixes
An automaton $\mathcal A = (X, Q, \delta, q_0)$ is called permutation-free iff no word $w \in X^*$ induces a nontrivial permutation of a subset of the states of $\mathcal A$. More formally for any $R \...
- 798
4
votes
1
answer
172
views
Subsets of $\omega$-regular lanuages accepted by automata with special acceptance condition
Let $\mathcal A = (X, Q, \delta, q_0, F)$ be a deterministic finite automata with the following acceptance condition on infinite words:
The automata accepts $\xi \in X^{\omega}$ with respect to $F$ ...
- 798
2
votes
1
answer
1k
views
Proof that the $\omega$-language consisting of all words containing every finite word as a factor is not rational/regular
Let $\eta$ be an $\omega$-word over $X = \{0,1\}$ and let $F_k(\eta)$ denote the factors of $\eta$ of length $k$. Define the following $\omega$-languages
$$
L_k := \{ \xi : F_k(\xi) = X^k \} = \{ \xi ...
- 798
2
votes
1
answer
197
views
Varieties of rational languages and (pseudo-)varieties of finite monoids, question regarding closure property
Let $\mathcal Rat(A)$ denote the class of rational (or regular) languages over the alphabet $A$, a subset $\mathcal V(A) \subseteq \mathcal Rat(A)$ is called a variety of (rational) languages iff
...
- 798
4
votes
1
answer
322
views
Is it decidable whether the support of a rational $\mathbb{Z}$-series is a regular language?
Let $S \in \mathbb{Z}\langle\langle A\rangle\rangle$ be a rational series in noncommutative variables. The support of $S$ is the set of all words $u \in A^*$ such that $(S, u) \not= 0$. It is ...
- 841
4
votes
0
answers
125
views
Properties of classical automata preserved in Büchi automata
Given two NFW $A$ and $B$, we regarded $A$ and $B$ as Büchi automata.
We can show that the containment property is not preserved in Büchi automata. That is, we can construct a example: $L(A) \...
- 73
12
votes
5
answers
3k
views
Generating function of a regular language
It is well known that the generating function of a regular language $L$, i.e. $\sum n_kz^k$ where $n_k$ is the number of words of length $k$ in $L$, is rational, i.e. a quotient of two polynomials $P(...
user6976
-1
votes
1
answer
7k
views
prove (a+b)*=a*(ba*)* [closed]
formal language and automata theory
regular expessions
(a+b)* =a*(ba*)*
please answer
I want the proof
thank you
- 9
4
votes
1
answer
2k
views
Deciding equivalence of regular languages
Given two regular expressions $R$ and $S$ on an alphabet $\Sigma$ it is possible to decide their equivalence as follows:
build two finite automata $M_R$ and $M_S$ such that $L(R) = L(M_R)$ and $L(S) =...
- 105
5
votes
0
answers
326
views
Büchi automata with acceptance strategy [closed]
I have already asked this question on cstheory.stackexchange, but without success. Maybe it is too close to an "open problem", although it is not a famous one. Anyway I try here, I can ...
- 1,341
1
vote
2
answers
2k
views
Translate a buchi automaton to LTL
How can I translate a Büchi automaton A to LTL(linear temporal logic) if $L(A)$ is definable in the LTL?
MY idea is : Büchi automaton $A$ ===> QPTL ===> LTL
I know that given any Buchi ...
- 73
3
votes
0
answers
893
views
Question about $\omega$-regular languages
As most of you already know, in model checking most linear-time properties are either safety properties or liveness properties. A linear time property is usually described with an $\omega$-regular ...
- 173
3
votes
2
answers
776
views
Certain type of regular languages
Dear All,
there is one type of regular languages, over $\{a,b\}$, which appear naturally in what I am studying, so if anybody could recognise them, or say any sort of their characterisation, that ...
- 1,437
13
votes
0
answers
274
views
Eilenberg's rational hiererchy of nonrational automata & languages — where is it now?
In the preface to his very influential books Automata, Languages and Machines (Volumes A, B), Samuel Eilenberg tantalizingly promised Volumes C and D dealing with "a hierarchy (called the rational ...
- 161
4
votes
2
answers
2k
views
Are context-free languages with context-free complements necessarily deterministic context-free?
Let $L \subseteq A^\star$ be a formal language over $A$ generated by a context-free grammar, and $L' = A^\star - L$ be the relative complement in $A^\star$.
If $L$ and $L'$ are both context-free, are ...
- 387
3
votes
1
answer
528
views
Study of free monoids of the recursive S. Eilenberg.
Compared to the usual treatises on recursion (eg, Rogers H. "Computability and Undecidability." McGraw-Hill, New York) the book of Samuel Eilenberg & Calvin C. Elgot "Recursiveness" treats such ...
- 4,165
7
votes
2
answers
622
views
Can you hide a letter without losing information?
Consider the following game between Alice and Bob.
$\Sigma$ is a finite nonempty alphabet, $\Delta \notin \Sigma$ denotes
a special symbol, and $k > 0$ is a positive integer constant representing
...
- 73
3
votes
3
answers
552
views
Finite variation and idempotent languages and automata
Let $L$ be a regular language over alphabet $\Sigma$ and let $A:=(Q,\Sigma,\delta, q_0, F)$ be the minimal DFA recognizing $L$. For every $w\in \Sigma^*$ define the variation of $w$ w.r.t. $L$ by
$$\...
- 424
6
votes
1
answer
516
views
Growth zeta-functions of regular languages
Dear All,
my following question may be known and ought to be known, so in case it is folklore please could you give me the references.
To start, it is obvious that growth of rational languages are ...
- 1,437
2
votes
1
answer
435
views
Given a PDA M such that L(M) is in DCFL construct a DPDA N such that L(N) = L(M)
Is it possible to construct an algorithm which takes as input a pushdown automaton $M$ along with the information that the language accepted by this automaton $L(M)$ is a deterministic context-free ...
- 143
12
votes
3
answers
877
views
Complementation of $\omega$-regular languages in reverse mathematics
Does anyone know where Büchi's theorem that $\omega$-regular languages are closed under complementation fits into the reverse-mathematics classification scheme? That is, is it equivalent over $\...
- 866
8
votes
2
answers
943
views
A special class of regular languages: "circular" languages. Is it known?
We can define a subclass of the regular languages. Fix an alphabet $\Sigma$. Define the "circular" languages (actually, the name already exists to denote a different thing it seems, used in the field ...
- 415
3
votes
3
answers
963
views
'Closure' of CFLs under complementation and intersection
Consider two context-free languages $L_1, L_2$. Of course, $L_1 - L_2, L_1\cap L_2, \bar{L}_1$, etc. are not necessarily context-free, but they are context-sensitive (the second is easy, the other two ...
- 793
27
votes
1
answer
1k
views
Automatic groups - recent progress
Epstein's (et al.) "Word Processing in Groups" is a quite comprehensive monograph on automatic groups, finite automata in geometric group theory, specific examples like braid groups, fundamental ...
- 2,449
11
votes
6
answers
3k
views
Regular languages and the pumping lemma
Let's say that I want to prove that a language is not regular.
The only general technique I know for doing this is the so-called "pumping lemma", which says that if $L$ is a regular language, then ...
- 44.8k