# Tagged Questions

1answer
109 views

### Counting the number of words accepted by an acyclic NFA

Let $M$ be an acyclic NFA. Since $M$ is acyclic, $L(M)$ is finite. Can we compute $|L(M)|$ in polynomial time? If not, can we approximate it? Note that the number of words is not the same as the ...
1answer
75 views

### Smallest NFA accepting concatenations of two words of the length $k$ which are different at all positions

Let $k\in \mathbb N$ I'm looking for a small NFA build for the language of concatenation of two words of the length $k$ which are index-wise different, i.e. L_k=\{u\cdot v \in \Sigma^* : ...
1answer
71 views

### A NPDA for the language $L = \{w \mid w \in \{a,b,c\}^*, n_c(w) = n_a(w) + n_b(w)\}$

Consider the language $L = \{w, w \in \{a,b,c\}^*, n_c(w) = n_a(w) + n_b(w)\}$, where $n_q(\omega)$ is defined to be "the number of $p \in \omega$. I have tried a couple of PDA's that follow this ...
3answers
86 views

### Relaxing the stack in a push down automata

Given a non-deterministic push down automata (we define "accept" here using accept states), if we assume any operation popping from the stack and checking if the top of the stack contains some symbol ...
2answers
135 views

### Push Down Automatons “guess” - what does that mean?

I realize non-deterministic pushdown automata can be an improvement over deterministic ones as they can "choose" among several states and there are some context-free languages which cannot be accepted ...
3answers
222 views

### Algorithm to shrink a DFA by introducing nondeterminism?

This is somewhat related to another question I asked, but I feel it's different enough to warrant its own question. I'm doing research where I'm trying to find the structure of complements of a ...
3answers
161 views

### Are there algorithms to exactly minimize NFAs which are sometimes efficient?

I'm doing some research with NFAs, and I'm wondering there are algorithms which quasi-efficiently minimize them. I realize that this problem is $PSPACE$ hard, so I'm not looking for a polynomial time ...
1answer
152 views

### Paper with proof that $L=\{ a^n b^n \mid n \geq 0 \} \cup \{ a^n b^{2n} \mid n \geq 0 \}$ is not Deterministic Context Free?

These lecture slides sketch a proof that $L=\{ a^n b^n \mid n \geq 0 \} \cup \{ a^n b^{2n} \mid n \geq 0 \}$ cannot be accepted by any Deterministic Pushdown Automaton. Unfortunately, the slides give ...
1answer
126 views

### Nondeterministic finite state machine without any initial state possible

Is it theoretically possible to have a nondeterministic finite state machine without any initial state or does it need at least one initial state?
2answers
110 views

### Classes of NFAs which allow efficient subset testing or unambiguity conversions

I'm doing some research regarding NFAs and inclusion problems with them. I know that in general, the inclusion problems, and converting to an unambiguous NFA, are both PSPACE-complete. I'm wondering, ...
4answers
619 views

### Words that have the same right- and left-associative product

I have started to study non deterministic automata using the book of Hopcroft and Ullman. I'm stuck in a problem that I found very interesting: Give a non deterministic finite automaton accepting ...
1answer
766 views

### Computational power of deterministic versus nondeterministic min-heap automata

This is a follow-up question of this one. In a previous question about exotic state machines, Alex ten Brink and Raphael addressed the computational capabilities of a peculiar kind of state machine: ...
3answers
710 views

### What are the conditions for a NFA for its equivalent DFA to be maximal in size?

We know that DFAs are equivalent to NFAs in expressiveness power; there is also a known algorithm for converting NFAs to DFAs (unfortunately I do now know the inventor of that algorithm), which in ...