# Questions tagged [automata-theory]

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

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### Can any c.e. language with infinite words be decomposed into infinite CFLs with infinite words?

Suppose $L$ is a computably enumerable language, can it be decompose into infinite CFLs with infinite words ? $$L=\bigcup_{L_i\in CFL }^{\infty}L_i$$ Second question: if it is possible that every $L$...
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### Is there an inherently ambiguous language which can not be recognized by Deterministic LBA?

Is there inherently ambiguous language which can not be recognized by Deterministic LBA? For example, $L=\{wv: w,v=(x|y)^*, w=w^R,v=v^R\}$, is there any deterministc LBA that recognizes $L$ ?
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### Equality Constraints over Sets with Tree Automata

Tree Automata can be used to model sets of values of a Herbrand Universe, for example, to model possible values in a functional program. Systems of subtype constraints over set expressions have ...
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### What is the motivation behind defining Deterministic Looping Automata?

I was wondering about what could possibly be the motivation behind defining the deterministic looping automata? What puzzles me is that they accept a word iff they have a run on it! I believe they ...
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### Automata recognizing $X^*$ for a finite code $X$

Let $\Sigma$ be a finite alphabet. A code $X$ over $\Sigma$ is a subset of $\Sigma^*$ such that each word in $X^*$ can be uniquely represented as a concatenation of words in $X$. A code $X$ is finite ...
907 views

### Quadratic relationship between nondeterministic and deterministic space?

Savitch's theorem shows that $\mathrm{NSPACE}(f(n)) \subseteq \mathrm{DSPACE}(f(n)^2)$ for all large enough functions $f$, and proving that this is tight has been an open problem for decades. Suppose ...
507 views

### In the context of regular languages, must the alphabet be finite?

In The Theory of Parsing, Translation, and Compiling, Volume I, Section 0.2.1 (p.15 / 1972), Aho and Ullman casually write that "[a]n alphabet need not be finite or even countable, but for all ...
268 views

### Number of minimal DFAs of size at most $m$?

Let $\Sigma$ be an alphabet of size $2$, and consider minimal DFAs whose size is bounded by at most $m$. Let $f(m)$ denote the number of different such minimal DFAs. Can we find a closed-form ...
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### CFGs in a certain normal form

Consider Context-Free Grammars with rules of the form $S\to\epsilon$ or $A\to aB | Ba|a$, meaning that any nonterminal other than $S$ can be replaced by a terminal, or by a pair of letters exactly one ...
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### Shortest string in the intersection of a context-free language and a regular language

For a language $X$, define $ss(X) = \min_{x\in X} |x|$, the length of the shortest string in $X$. For simplicity, we define $ss(\emptyset)=0$. Let $L$ be a context-free language generated by a context-...
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### Mastery-based grading for Theory of Computation

I would be interested to learn of anyone's experience using mastery-based (or "mastery-level") grading in a Theory of Computation course. Usually this requires—at a minimum— a detailed ...
248 views

### Partition refinement in transition state systems (bisimulation contraction)

I am trying to understand bisimulation contraction of Kripke models. I have read these lecture slides and this Wikipedia page, but I still don't fully understand it. I can understand that the two ...
328 views

### Is this a regular relation?

I'm a linguist (and not a computer scientist!) investigating a new sort of linguistic formalism for mapping phonological strings into other strings - and I'm wondering if it's a regular relation that ...
168 views

### Hysteresis in finite automata

The concept of hysteresis seems well suited to describe and distinguish finite automata: "Hysteresis is the dependence of the state of a system on its history." (Wikipedia, Hysteresis) "[The ...
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### A reference for a “more algebraic” approach to pushdown automata and CFLs?

In the Sakarovitch's book on automata theory, it is written in the introduction to the section on rationals in the free group that the material presented therein lays "the foundation of a truly ...
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### Finite Automata with succinct representation of chains of states

Consider a kind of automata similar to common DFAs or NFAs where it is possible to represent succinctly linear chains of states. In other words, an automaton like this: could be represented in this ...
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### Formal definition of Turing Completeness [closed]

Wikipedia states: In computability theory, a system of data-manipulation rules […] is said to be Turing complete or computationally universal if it can be used to simulate any single-taped Turing ...
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### Hierarchies in regular languages

Is there any known "nice" hierarchy $L_0 \subseteq L_1 \subseteq L_2 \subseteq \dots$ (may be finite) inside the class of regular languages $L$? By nice here, the classes in each hierarchy capture ...
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### Is there a well-defined division operation on finite automata?

Background: Given two deterministic finite automata A and B, we form the product C by letting the states in C be the cartesian product of states in A and states in B. Then, we choose transitions, ...
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### Characterization of union of DCFLs

We know that DCFL is not closed under the union operation and CFL is closed under union and contains the union of DCFLs. Is there a characterization of finite unions of DCFLs?
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### Useful equivalence relations on $X^{\ast}$ (like the Nerode and syntactic equivalence relations)

I want to have an overview of all the meaningful equivalence relations defined on $X^{\ast}$, in particular when the languages in question are regular. They typically arise in connection with the ...
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### Kleene closure of DFA

Given an $n$-state DFA (over a binary or any fixed alphabet), what is the complexity of computing its Kleene closure DFA? What is the largest possible/known blow-up in the number of states?
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### For which regular expressions $\alpha$ is $\{ \beta \mid L(\alpha) = L(\beta) \}$ PSPACE-complete?

It is well known that the following problem is PSPACE-complete: Given regular expression $\beta$, does $L(\beta) = \Sigma^*$? What about determining equivalence to other (fixed) regular ...
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### Current research topics in tree automata

What are current research topics connected with tree automata? I'm particularly interested with connection between automatas, logics and databases. Kind regards, XYZ
### Simplest Machine Model Accepting $L = \{ww^Rw\;|\; w\in \Sigma^*\}$
Let $\Sigma$ be a finite alphabet. A trivial finite automaton can accept the language $L_1 = \{w\;|\;w\in \Sigma^*\}$. A simple pushdown automaton can accept the language \$L_2 = \{ww^R\;|;w\in \...