DERIVWWW - WEB-BASED SYMBOLIC DIFFERENTIATION SYSTEM

The article presents an online system for symbolic differentiation. It shows how derivatives are calculated. The trees are used for internal representation of formulas. Derivatives are generated by tree transformations. Presented algorithms are part of the microsystems simulator Dero. They are required by the calculation algorithms such as Newton-Raphson. They can be used to generate derivatives in model description languages and for automatic derivative calculation. DerivWWW can be used in didactics. The system can serve as a tool for students to count function derivatives at the point. It can also be used in teaching on the technical fields of study. Symbolic derivatives are saved in the Tex format, allowing easy integration with other software. The developed and implemented algorithms are discussed. Examples of use are given.

Visibly Pushdown Transducers with Well-Nested Outputs

Visibly pushdown transducers (VPTs) are visibly pushdown automata extended with outputs. They have been introduced oto model transformations of nested words, i.e. words with a call/return structure. When outputs are also structured and well nested words, VPTs are a natural formalism to express tree transformations evaluated in streaming. We prove the class of VPTs with well-nested outputs to be decidable in PTIME. Moreover, we show that this class is closed under composition and that its type-checking against visibly pushdown languages is decidable.