# Questions tagged [automata-theory]

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

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### Finding the smallest DFA that separates two words without using brute force search?

Given two strings x and y, I want to build a minimum size DFA that accepts x and rejects y. One way to do this is brute force search. You enumerate DFA's starting with the smallest. You try each ...
244 views

### computing maximal bit density over a FSM

let $L$ be a regular language defined by a FSM over binary symbols $\{0,1\}$. consider a function $f(x)$ on words/ strings that computes "bit density", defined as the number of $1$'s in a word ("...
825 views

### DFA intersection algorithm for special cases

I'm interested in efficient algorithms for DFA intersection for special cases. Namely, when the DFAs to intersect obey a certain structure and/or operates on limited alphabet. Is there any source ...
419 views

### Minimizing Automata accepting $\omega$-words (i.e. infinite words)

What is the standard approach on minimizing Büchi-Automata (or also Müller-Automata)? Transfering the usual technique from finite words, i.e. setting two states to be equal if the words "running out" ...
114 views

### Extensional characterization of non-deterministic finite state transductions

I recently became aware of the rather appealing characterization of deterministic word-to-word transductions as word functions with bounded variation (see e.g. ). This coincides with the set of ...
247 views

### Alternating tree automata for arbitrary arity tree

Could alternating tree automata be used for recognizing set (language) of arbitrary-arity trees? More specifically, as an example: let $\Sigma = \{a,b,c\}$ - labels for tree nodes. Trees from $T$ ...
310 views

### Pseudorandom generator for finite automata

Let $d$ be a constant. How can we provably construct a pseudorandom generator that fools $d$-state finite automata? Here, a $d$-state finite automata has $d$ nodes, a start node, a set of nodes ...
1k views

### What is the worst-case runtime complexity to transform a NFA to DFA via Rabin-Scott's power set construction?

What is the worst-case runtime complexity to transform a NFA to DFA via Rabin-Scott's power set construction? Why? Details: http://en.wikipedia.org/wiki/Powerset_construction states that the worst-...
963 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 ...
163 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 ...
1k views

### How to XOR automata? [closed]

Say we have 3 DFAs. We know how to OR, AND, or NOT them. But how does one XOR them? There is not one single mention of this online. x XOR y XOR z = ((x|y)(~x|y)|z) (~((x|y)(~x|y))|z). This is way too ...
762 views

### Are regular languages closed under addition?

Specifically what I mean by addition is, we define $\Sigma_i$ to be the alphabet $\{0, 1, 2, ..., i\}$. Given regular languages $A$ and $B$ under some alphabet $\Sigma_i$, look at $A\times B$. For ...
236 views

### Automata and a kind of pumping lemma on state transition function

We encountered this question as an exercise in a Büchi automata book a couple of decades ago, and back then gave a few tries thinking that it should be easy. But haven't seen a solution. My ...
515 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 ...
518 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 ...
144 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 ...
300 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 ...
166 views

### Example of a $U^\omega$ that is not Deterministic Büchi recognizable

Is there a regular language $U$, for which $U^\omega$ is not a Deterministic Büchi recognizable language. I have been thinking over it for some time, but have been unable to come up with an example.
130 views

### finite automata under morphism [closed]

Given two (deterministic) finite automata $A, B$ over $\Sigma$, a mapping $h:\Sigma\rightarrow \Sigma'$ Naturally $h$ can be extended to a mapping in $\Sigma^*\rightarrow \Sigma'^*$ which is denoted ...
166 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 ...
253 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 $LR(1)$. ...
162 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 ...
651 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 ...
426 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 ...
122 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 ...
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.
645 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 ...
494 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 ...
253 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 ...
369 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 ...
461 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 $Q(A)$, i.e....
254 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 ...
1k 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 $2 \times 10^6$ ...
433 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 ...
236 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 ...
310 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?
543 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 ...
8k 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. ...
116 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. ...
277 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. ...
76 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 ...
567 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 ...
255 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 ...
163 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 ...
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### 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 ...