Search arXiv⌕ Search

SEARCH · Search arXiv

Results for “cs.FL”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6Linked to original sources
arXiv2010

Evolving MultiAlgebras unify all usual sequential computation models

It is well-known that Abstract State Machines (ASMs) can simulate "step-by-step" any type of machines (Turing machines, RAMs, etc.). We aim to overcome two facts: 1) simulation is not identification, 2) the ASMs simulating machines of some type do not constitute a natural class among all ASMs. We modify Gurevich's notion of ASM to that of EMA ("Evolving MultiAlgebra") by replacing the program (which is a syntactic object) by a semantic object: a functional which has to be very simply definable over the static part of the ASM. We prove that very natural classes of EMAs correspond via "literal identifications" to slight extensions of the usual machine models and also to grammar models. Though we modify these models, we keep their computation approach: only some contingencies are modified. Thus, EMAs appear as the mathematical model unifying all kinds of sequential computation paradigms.

cs.FL↗
arXiv2010

Deriving the Probabilistic Capacity of General Run-Length Sets Using Generating Functions

In "Reliable Communication in the Absence of a Common Clock" (Yeung et al., 2009), the authors introduce general run-length sets, which form a class of constrained systems that permit run-lengths from a countably infinite set. For a particular definition of probabilistic capacity, they show that probabilistic capacity is equal to combinatorial capacity. In the present work, it is shown that the same result also holds for Shannon's original definition of probabilistic capacity. The derivation presented here is based on generating functions of constrained systems as developed in "On the Capacity of Constrained Systems" (Boecherer et al., 2010) and provides a unified information-theoretic treatment of general run-length sets.

cs.IT↗
arXiv2010

Bulking II: Classifications of Cellular Automata

This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation between cellular automata and study the quasi-order structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasi-orders are considered (induced equivalence relations, maximum elements, induced orders, etc) providing several formal tools allowing to classify cellular automata.

cs.FL↗
arXiv2010

Parikh Images of Regular Languages: Complexity and Applications

We show that the Parikh image of the language of an NFA with n states over an alphabet of size k can be described as a finite union of linear sets with at most k generators and total size 2^{O(k^2 log n)}, i.e., polynomial for all fixed k >= 1. Previously, it was not known whether the number of generators could be made independent of n, and best upper bounds on the total size were exponential in n. Furthermore, we give an algorithm for performing such a translation in time 2^{O(k^2 log(kn))}. Our proof exploits a previously unknown connection to the theory of convex sets, and establishes a normal form theorem for semilinear sets, which is of independent interests. To complement these results, we show that our upper bounds are tight and that the results cannot be extended to context-free languages. We give four applications: (1) a new polynomial fragment of integer programming, (2) precise complexity of membership for Parikh images of NFAs, (3) an answer to an open question about polynomial PAC-learnability of semilinear sets, and (4) an optimal algorithm for LTL model checking over discrete-timed reversal-bounded counter systems.

cs.LO↗
arXiv2010

Algebraic Linear Orderings

An algebraic linear ordering is a component of the initial solution of a first-order recursion scheme over the continuous categorical algebra of countable linear orderings equipped with the sum operation and the constant 1. Due to a general Mezei-Wright type result, algebraic linear orderings are exactly those isomorphic to the linear ordering of the leaves of an algebraic tree. Using Courcelle's characterization of algebraic trees, we obtain the fact that a linear ordering is algebraic if and only if it can be represented as the lexicographic ordering of a deterministic context-free language. When the algebraic linear ordering is a well-ordering, its order type is an algebraic ordinal. We prove that the Hausdorff rank of any scattered algebraic linear ordering is less than $ω^ω$. It follows that the algebraic ordinals are exactly those less than $ω^{ω^ω}$.

cs.FL↗
arXiv2010

On the Minimal Uncompletable Word Problem

Let S be a finite set of words over an alphabet Sigma. The set S is said to be complete if every word w over the alphabet Sigma is a factor of some element of S*, i.e. w belongs to Fact(S*). Otherwise if S is not complete, we are interested in finding bounds on the minimal length of words in Sigma* which are not elements of Fact(S*) in terms of the maximal length of words in S.

cs.FL↗
arXiv2010

A proof Procedure for Testing Membership in Regular Expressions

We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the complex conversion process from regular expressions to finite automata is not needed. As a consequence, our algorithm is simple and extends easily to various extensions to regular expressions such as timed regular expressions or regular languages with the intersection.

cs.FL↗
arXiv2026

Digital Circuits as Moore Machines

This paper illustrates a technique for specifying the timing, logical operation, and compositional circuit design of digital circuits in terms of ordinary state machines with output (Moore machines). The method is illustrated here with specifications of gates, latches, and other simple circuits and via the construction of devices starting with a SR latch built from gates. The method is based on "classical" automata and recursive functions on strings (sequential functions).

cs.FL↗
arXiv2010

Complexity of Problems for Commutative Grammars

We consider Parikh images of languages accepted by non-deterministic finite automata and context-free grammars; in other words, we treat the languages in a commutative way --- we do not care about the order of letters in the accepted word, but rather how many times each one of them appears. In most cases we assume that the alphabet is of fixed size. We show tight complexity bounds for problems like membership, equivalence, and disjointness. In particular, we show polynomial algorithms for membership and disjointness for Parikh images of non-deterministic finite automata over fixed alphabet, and we show that equivalence is Pi2P complete for context-free grammars over fixed terminal alphabet.

cs.FL↗
arXiv2010

A Characterization of Combined Traces Using Labeled Stratified Order Structures

This paper defines a class of labeled stratified order structures that characterizes exactly the notion of combined traces (i.e., comtraces) proposed by Janicki and Koutny in 1995. Our main technical contributions are the representation theorems showing that comtrace quotient monoid, combined dependency graph (Kleijn and Koutny 2008) and our labeled stratified order structure characterization are three different and yet equivalent ways to represent comtraces.

cs.DC↗
arXiv2010

The Isomorphism Problem for omega-Automatic Trees

The main result of this paper is that the isomorphism for omega-automatic trees of finite height is at least has hard as second-order arithmetic and therefore not analytical. This strengthens a recent result by Hjorth, Khoussainov, Montalban, and Nies showing that the isomorphism problem for omega-automatic structures is not $Σ^1_2$. Moreover, assuming the continuum hypothesis CH, we can show that the isomorphism problem for omega-automatic trees of finite height is recursively equivalent with second-order arithmetic. On the way to our main results, we show lower and upper bounds for the isomorphism problem for omega-automatic trees of every finite height: (i) It is decidable ($Π^0_1$-complete, resp,) for height 1 (2, resp.), (ii) $Π^1_1$-hard and in $Π^1_2$ for height 3, and (iii) $Π^1_{n-3}$- and $Σ^1_{n-3}$-hard and in $Π^1_{2n-4}$ (assuming CH) for all n > 3. All proofs are elementary and do not rely on theorems from set theory.

cs.LO↗
arXiv2011

Measuring and Synthesizing Systems in Probabilistic Environments

Often one has a preference order among the different systems that satisfy a given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is preferred if it generates a higher expected value. We solve the following optimal-synthesis problem: given an omega-regular specification, a Markov chain that describes the distribution of inputs, and a weighted automaton that measures how well a system satisfies the given specification under the given input assumption, synthesize a system that optimizes the measured value. For safety specifications and measures given by mean-payoff automata, the optimal-synthesis problem amounts to finding a strategy in a Markov decision process (MDP) that is optimal for a long-run average reward objective, which can be done in polynomial time. For general omega-regular specifications, the solution rests on a new, polynomial-time algorithm for computing optimal strategies in MDPs with mean-payoff parity objectives. Our algorithm generates optimal strategies consisting of two memoryless strategies and a counter. This counter is in general not bounded. To obtain a finite-state system, we show how to construct an ε-optimal strategy with a bounded counter for any ε>0. We also show how to decide in polynomial time if we can construct an optimal finite-state system (i.e., a system without a counter) for a given specification. We have implemented our approach in a tool that takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. We present experimental results showing optimal systems that were generated in this way.

cs.LO↗
arXiv2010

On building minimal automaton for subset matching queries

We address the problem of building an index for a set $D$ of $n$ strings, where each string location is a subset of some finite integer alphabet of size $σ$, so that we can answer efficiently if a given simple query string (where each string location is a single symbol) $p$ occurs in the set. That is, we need to efficiently find a string $d \in D$ such that $p[i] \in d[i]$ for every $i$. We show how to build such index in $O(n^{\log_{σ/Δ}(σ)}\log(n))$ average time, where $Δ$ is the average size of the subsets. Our methods have applications e.g.\ in computational biology (haplotype inference) and music information retrieval.

cs.FL↗
arXiv2010

Construction of minimal DFAs from biological motifs

Deterministic finite automata (DFAs) are constructed for various purposes in computational biology. Little attention, however, has been given to the efficient construction of minimal DFAs. In this article, we define simple non-deterministic finite automata (NFAs) and prove that the standard subset construction transforms NFAs of this type into minimal DFAs. Furthermore, we show how simple NFAs can be constructed from two types of patterns popular in bioinformatics, namely (sets of) generalized strings and (generalized) strings with a Hamming neighborhood.

cs.FL↗
arXiv2010

An undecidable property of context-free languages

We prove that there exists no algorithm to decide whether the language generated by a context-free grammar is dense with respect to the lexicographic ordering. As a corollary to this result, we show that it is undecidable whether the lexicographic orderings of the languages generated by two context-free grammars have the same order type.

cs.FL↗