Regular Sensing
نویسندگان
چکیده
The size of deterministic automata required for recognizing regular and ω-regular languages is a well-studied measure for the complexity of languages. We introduce and study a new complexity measure, based on the sensing required for recognizing the language. Intuitively, the sensing cost quantifies the detail in which a random input word has to be read in order to decide its membership in the language. We show that for finite words, size and sensing are related, and minimal sensing is attained by minimal automata. Thus, a unique minimal-sensing deterministic automaton exists, and is based on the language’s right-congruence relation. For infinite words, the minimal sensing may be attained only by an infinite sequence of automata. We show that the optimal limit cost of such sequences can be characterized by the language’s right-congruence relation, which enables us to find the sensing cost of ω-regular languages in polynomial time. 1998 ACM Subject Classification F.4.3 Formal Languages, B.8.2 Performance Analysis and Design Aids, F.1.1 Models of Computation
منابع مشابه
Adapting physical carrier sensing to maximize spatial reuse in 802.11 mesh networks
Spatial reuse in a mesh network can allow multiple communications to proceed simultaneously, hence proportionally improve the overall network throughput. To maximize spatial reuse, the MAC protocol must enable simultaneous transmitters to maintain the minimal separation distance that is sufficient to avoid interference. This paper demonstrates that physical carrier sensing enhanced with a tunab...
متن کاملCompressed sensing snapshot spectral imaging by a regular digital camera with an added optical diffuser.
We propose a spectral imaging method that allows a regular digital camera to be converted into a snapshot spectral imager by equipping the camera with a dispersive diffuser and with a compressed sensing-based algorithm for digital processing. Results of optical experiments are reported.
متن کاملDetection of Human Movements with Pressure Floor Sensors
Following the recent Internet of Everything (IoE) trend, several general-purpose devices have been proposed to acquire as much information as possible from the environment and from people interacting with it. Among the others, sensing floors are recently attracting the interest of the research community. In this paper, we propose a new model to store and process floor data. The model does not a...
متن کاملOn Practical Regular Expressions
We report on simulation, hierarchy, and decidability results for Practical Regular Expressions (PRE), which may include back references in addition to the standard operations union, concatenation, and star. The following results are obtained: • PRE can be simulated by the classical model of nondeterministic finite automata with sensing one-way heads. The number of heads depends on the number of...
متن کاملThe Sensing Cost of Monitoring and Synthesis
In [2], we introduced sensing as a new complexity measure for the complexity of regular languages. Intuitively, the sensing cost quantifies the detail in which a random input word has to be read by a deterministic automaton in order to decide its membership in the language. In this paper, we consider sensing in two principal applications of deterministic automata. The first is monitoring: we ar...
متن کامل