There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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[서평]「Computer Organization and Design, The Hardware/Software Interface」

Chapter 8 establishes the relationship between the input and output power spectral densities of a linear system. Limitations on results are carefully detailed and the case of oscillator noise is considered. The theory is extended to multiple input-multiple output systems.

Linear System Theory

The computational power of networks of small resource-limited mobile agents is explored. Two new models of computation based on pairwise interactions of finite-state agents in populations of finite but unbounded size are defined. With a fairness condition on interactions, the concept of stable computation of a function or predicate is defined. Protocols are given that stably compute any predicate in the class definable by formulas of Presburger arithmetic, which includes Boolean combinations of threshold-k, majority, and equivalence modulo m. All stably computable predicates are shown to be in NL. Assuming uniform random sampling of interacting pairs yields the model of conjugating automata. Any counter machine with O (1) counters of capacity O (n) can be simulated with high probability by a conjugating automaton in a population of size n. All predicates computable with high probability in this model are shown to be in P; they can also be computed by a randomized logspace machine in exponential time. Several open problems and promising future directions are discussed.

Computation in networks of passively mobile finite-state sensors

This paper proposes a way to incorporate the idea of spiking neurons into the area of membrane computing, and to this aim we introduce a class of neural-like P systems which we call spiking neural P systems (in short, SN P systems). In these devices, the time (when the neurons fire and/or spike) plays an essential role. For instance, the result of a computation is the time between the moments when a specified neuron spikes. Seen as number computing devices, SN P systems are shown to be computationally complete (both in the generating and accepting modes, in the latter case also when restricting to deterministic systems). If the number of spikes present in the system is bounded, then the power of SN P systems falls drastically, and we get a characterization of semilinear sets. A series of research topics and open problems are formulated.

/pdf/spiking-neural-p-systems-63ihtdu60m.pdf

Spiking Neural P Systems

We introduce discrete pushdown timed automata that are timed automata with integer-valued clocks augmented with a pushdown stack. A configuration of a discrete pushdown timed automaton includes a control state, finitely many clock values and a stack word. Using a pure automata-theoretic approach, we show that the binary reachability (i.e., the set of all pairs of configurations (α,β), encoded as strings, such that α can reach β through 0 or more transitions) can be accepted by a nondeterministic pushdown machine augmented with reversal-bounded counters (NPCM). Since discrete timed automata with integer-valued clocks can be treated as discrete pushdown timed automata without the pushdown stack, we can show that the binary reachability of a discrete timed automaton can be accepted by a nondeterministic reversal-bounded multicounter machine. Thus, the binary reachability is Presburger. By using the known fact that the emptiness problem is decidable for reversal-bounded NPCMs, the results can be used to verify a number of properties that can not be expressed by timed temporal logics for discrete timed automata and CTL* for pushdown systems.

/pdf/binary-reachability-analysis-of-discrete-pushdown-timed-2s1vm0u8hf.pdf

Binary Reachability Analysis of Discrete Pushdown Timed Automata

https://eecs.wsu.edu/~zdang/papers/danga.pdf

Pushdown timed automata: a binary reachability characterization and safety verification

We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachability (i.e., the set of all pairs of configurations such that one can reach the other) of a PTA. Since a timed automaton can be treated as a PTA without the pushdown stack, we can show that the binary reachability of a timed automaton is definable in the additive theory of reals and integers. The results can be used to verify a class of properties containing linear relations over both dense variables and unbounded discrete variables. The properties previously could not be verified using the classic region technique nor expressed by timed temporal logics for timed automata and CTL$^*$ for pushdown systems. The results are also extended to other generalizations of timed automata.

Pushdown Timed Automata: a Binary Reachability Characterization and Safety Verification

https://eecs.wsu.edu/~zdang/papers/catalytic.pdf

Zhe Dang

Papers

Binary Reachability Analysis of Discrete Pushdown Timed Automata

Pushdown timed automata: a binary reachability characterization and safety verification

Pushdown Timed Automata: a Binary Reachability Characterization and Safety Verification

Catalytic P systems, semilinear sets, and vector addition systems

Counter machines and verification Problems