Cewei Cui

Similarity in languages and programs

We use an information-theoretic notion, namely, (Shannon) information rate, to generalize common syntactic similarity metrics (like Hamming distance and longest common subsequences) between strings to ones between languages. We show that the similarity metrics between two regular languages are computable. We further study self-similarity of a regular language under various similarity metrics. As far as semantic similarity is concerned, we study the amplitude of an automaton, which intuitively characterizes how much a typical execution of the automaton fluctuates. Finally, we investigate, through experiments, how to measure similarity between two real-world programs using Lempel-Ziv compression on the runs at the assembly level.

Execution information rate for some classes of automata

We study the Shannon information rate of accepting runs of various forms of automata. This rate is a complexity indicator for executions of these automata. Accepting runs of finite automata and reversal-bounded nondeterministic counter machines, as well as their restrictions and variations, are investigated and are shown, in many cases, to have computable execution rates. We also study the information rate of behaviors in discrete timed automata. We conduct experiments on C programs showing that estimating the information rates for their executions is feasible in many cases.

Information Rate of Some Classes of Non-regular Languages: An Automata-Theoretic Approach

We show that the information rate of the language accepted by a reversal-bounded deterministic counter machine is computable. For the nondeterministic case, we provide computable upper bounds. For the class of languages accepted by multi-tape deterministic finite automata, the information rate is computable as well.

ZERO-KNOWLEDGE BLACKBOX TESTING: WHERE ARE THE FAULTS?

We derive a quantitative relationship between the maximal entropy rate achieved by a blackbox software systems specification graph, and the probability of faults Pn obtained by testing the system, as a function of the length n of a test sequence. By equating “blackbox” to the maximal entropy principle, we model the specification graph as a Markov chain that, for each distinct value of n, achieves the maximal entropy rate for that n. Hence the Markov transition probability matrices are not constant in n, but form a sequence of transition matrices T1,…, Tn. We prove that, for nontrivial specification graphs, the probability of finding faults goes asymptotically to zero as the test length n increases, regardless of the evolution of Tn. This implies that zero-knowledge testing is practical only for small n. We illustrate the result using a concrete example of a system specification graph for an autopilot control system, and plot its curve Pn.

Typical Paths of a Graph

We introduce (finite and infinite) typical paths of a graph and prove that the typical paths carry all information with probability 1, asymptotically. An automata-theoretic characterization of the typical paths is shown: finite typical paths can be accepted by reversal-bounded multicounter automata and infinite typical paths can be accepted by counting Buchi automata (a generalization of reversal-bounded multicounter automata running on ω-words). We take a statechart example to show how to generate typical paths from a graph using SPIN model checker. The results are useful in automata theory since one can identify an information-concentrated-core of a regular language such that only words in the information-concentrated-core carry nontrivial information. When the graph is used to specify the system under test, the results are also useful in software testing by providing an information-theoretic approach to select test cases that carry nontrivial information of the system specification.

Lossiness of Communication Channels Modeled by Transducers

We provide an automata-theoretic approach to analyzing an abstract channel modeled by a transducer and to characterizing its lossy rates. In particular, we look at related decision problems and show the boundaries between the decidable and undecidable cases.

Execution Information Rate for Some Classes of Automata

We study the Shannon information rate of accepting runs of various forms of automata. The rate is therefore a complexity indicator for executions of the automata. Accepting runs of finite automata and reversal-bounded nondeterministic counter machines, as well as their restrictions and variations, are investigated and are shown, in many cases, with computable execution rates. We also conduct experiments on C programs showing that estimating information rates for their executions is feasible in many cases.

Information rate of some classes of non-regular languages: An automata-theoretic approach

Abstract We show that the information rate of the language accepted by a reversal-bounded deterministic counter machine is computable. For the nondeterministic case, we provide computable upper bounds. For the class of languages accepted by multi-tape deterministic finite automata, the information rate is computable as well.

A Free Energy Foundation of Semantic Similarity in Automata and Languages

This paper develops a free energy theory from physics including the variational principles for automata and languages and also provides algorithms to compute the energy as well as efficient algorithms for estimating the nondeterminism in a nondeterministic finite automaton. This theory is then used as a foundation to define a semantic similarity metric for automata and languages. Since automata are a fundamental model for all modern programs while languages are a fundamental model for the programs’ behaviors, we believe that the theory and the metric developed in this paper can be further used for real-word programs as well.