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Symbolic Automata: The Toolkit
Margus Veanes and Nikolaj Bjørner
Microsoft Research, Redmond, WA
Abstract.The symbolic automata toolkit lifts classical automata anal-ysis to work modulo rich alphabet theories. It uses the power of state-of-the-art constraint solvers for automata analysis that is both expres-sive and efficient, even for automata over large finite alphabets. The toolkit supports analysis of finite symbolic automata and transducers over strings. It also handles transducers with registers. Constraint solving is used when composing and minimizing automata, and a much deeper and powerful integration is also obtained by internalizing automata as 1 theories. The toolkit, freely available from Microsoft Research , has re-cently been used in the context of web security for analysis of potentially malicious data over Unicode characters.
Introduction.The distinguishing feature of the toolkit is the use and oper-ations with symbolic labels. This is unlike classical automata algorithms that mostly work assuming a finite alphabet. Adtantages of a symbolic representa-tion are examined in [4], where it is shown that the symbolic algorithms con-sistently outperform classical algorithms (often by orders of magnitude) when alphabets are large. Moreover, symbolic automata can also work with infinite alphabets. Typical alphabet theories can bearithmetic(over integers, rationals, bit-vectors),algebraic data-types(for tuples, lists, trees, finite enumerations), andarrays. Tuples are used for handling alphabets that are cross-products of multiple sorts. In the following we describe the core components and functional-ity of the tool. The main components areAutomatonhTi, basic automata opera-tions modulo a Boolean algebraT;SFAhTi, symbolic finite automata as theories moduloT; andSFThTi, symbolic finite transducers as theories moduloT. We illustrate the tool’s API using code samples from the distribution.
AutomatonhTi.The main building block of the toolkit, that is also defined as a corresponding generic class, is a (symbolic) automaton overT:AutomatonhTi. The typeTis assumed to be equipped with effective Boolean operations over T:,,¬,,isthat satisfy the standard axioms of Boolean algebras, where is(ϕ) checks if a termϕis false (thus, to check ifϕis true, checkis(¬ϕ)). The main operations overAutomatonhTiare(intersection),(union){(com-plementation),A≡ ∅(emptiness check). As an example of a simple symbolic operation consider products: whenA, Bare of typeAutomatonhTi, thenAB 0 00 has the transitionsh(p, q), ϕψ,(p ,q)ifor each transitionhp, ϕ, pi ∈A, and 1 The binary release is available fromhttp://research.microsoft.com/automata.