Questions tagged [automata-theory]

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

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Fast weighted intersection algorithm for CFG and FSA with self loops but no other circles?

We all know that arbitrary CFG and FSA can be intersected using the Bar-Hillel Construction, whose time complexity is unfortunately too expensive. On the other hand, there are efficient algorithms ...
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62 views

Rational power series over $\mathbb N \cup \{\infty\}$, rationality of singular part

Let $\Sigma$ be a finite alphabet, and consider the formel power series over $\Sigma$ considered as non-commuting variables with coefficients in the semiring $\mathcal N := \mathbb N \cup \{\infty\}$ ...
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457 views

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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102 views

Relation between MDPs and non-deterministic finite automatons

I'm confused as to the relation (computability-wise) between markov decision processes and NFAs. Are finite state MDPs expressible as regular grammars? If so, are markov decision processes thus ...
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102 views

Convenient forms of Turing machines

Let us suppose that I have defined a new convenient form of the Turing machine for processing of some specific sort of commonly used structures. This form of TM contains some specific features ...
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175 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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127 views

Why is an automaton on finite words co-deterministic iff its transitions are co-deterministic

In the article Automata and semigroups recognizing infinite words an automaton is specified by $\mathcal A = (Q, A, E, I, F)$ where $I$ is a set of initial states and $F$ a set of final states, $Q$ ...
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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.
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94 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 ...
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73 views

Vector representation of probabilistic automaton

Suppose we have $N$ states $q_i$, $0\leq i<N$ Suppose we have $N\times N$ probability matrix $p_{ij}$, $0\leq i<N$, $0\leq j<N$, And suppose a machine, which is being in state $q_i$ then ...
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91 views

Automatic structures/functions: Is (Z,+) under a unary representation automatic?

The group $(\mathbb{Z}, +)$ is automatic (ala Khoussainov) when using the "standard" representation in a decimal base. But if I want to use a different representation of Z, encoding my integers with ...
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190 views

Dynamic k-shortest paths in a weighted transducer

I'm looking for references relating to dynamically computing the k-shortest output paths through a stochastic, acyclic, weighted transducer that is being constructed on-the-fly. In this scenario ...
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637 views

Strategy for grammar derivation of a formal language

I wonder, whether there is any strategy/ies for grammar derivation of a formal language. I'd be thankful, if you give me some hints, tips on how should one "think" trying to find a grammar. I'm ...
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180 views

Edit-Distance of weighted automata

I'm trying to understand "Edit Distance of Weighted Automata" by Mehryar Mohri: [83], [93] and [99] at http://www.cs.nyu.edu/~mohri/pub/ (they are virtually identical so which of them doesn't matter). ...
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68 views

Language recongized by a “quasi realtime register machine”?

Counter machines are very powerful. Even two counters suffice for making these Turing complete. But, in simulating a Turing machine the counter machine encodes in its integers a large amount of data. ...
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151 views

Questions about the definition of the Quantum Turing Machine

I am trying to have a better understanding of the definition of the Quantum Turing Machine. My questions: If the output of a quantum program is the eigenvalue of the ground state of a Hamiltonian ...
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210 views

formal definition of “flowcharts”

I am looking for a formal definition of so-called "flowcharts" used as representation of programs or business processes. Is there some good one around ? Thx JCLL

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