https://www.inf.ed.ac.uk/teaching/courses/seoc/2005_2006/resources/statecharts.pdf

Statecharts: A visual formalism for complex systems

https://hal.inria.fr/inria-00075711/document

The ESTEREL synchronous programming language: design, semantics, implementation

From the Publisher:
Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical first-order predicate calculus. Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value. It can be used for formalizing correctness specifications and proving rigorously that those specifications are met by a particular program. Other uses include determining the equivalence of programs, comparing the expressive power of various programming constructs, and synthesizing programs from specifications. 
This book provides the first comprehensive introduction to Dynamic Logic. It is divided into three parts. The first part reviews the appropriate fundamental concepts of logic and computability theory and can stand alone as an introduction to these topics. The second part discusses PDL and its variants, and the third part discusses DL and its variants. Examples are provided throughout, and exercises and a short historical section are included at the end of each chapter.

Dynamic Logic

The higraph, a general kind of diagramming object, forms a visual formalism of topological nature. Higraphs are suited for a wide array of applications to databases, knowledge representation, and, most notably, the behavioral specification of complex concurrent systems using the higraph-based language of statecharts.

On visual formalisms

http://www.workflowpatterns.com/documentation/documents/yawl_qut_report_FIT-TR-2002-06.pdf

YAWL: yet another workflow language

STATEMATE is a set of tools, with a heavy graphical orientation, intended for the specification, analysis, design, and documentation of large and complex reactive systems. It enables a user to prepare, analyze, and debug diagrammatic, yet precise, descriptions of the system under development from three interrelated points of view, capturing structure, functionality, and behavior. These views are represented by three graphical languages, the most intricate of which is the language of statecharts, used to depict reactive behavior over time. In addition to the use of statecharts, the main novelty of STATEMATE is in the fact that it understands the entire descriptions perfectly, to the point of being able to analyze them for crucial dynamic properties, to carry out rigorous executions and simulations of the described system, and to create running code automatically. These features are invaluable when it comes to the quality and reliability of the final outcome. >

/pdf/statemate-a-working-environment-for-the-development-of-1w9uawvlqd.pdf

STATEMATE: a working environment for the development of complex reactive systems

On the Formal Semantics of Statecharts (Extended Abstract)

Two extensions of propositional dynamic logic for dealing with infinite computations, LPDL and RPDL, are compared in expressive power. The first is obtained by adding the assertion loop (α) for any program α, meaning “α contains an infinite computation,≓ and the second by adding repeat (α), meaning “α can be repeated indefinitely.≓ While repeat can be used to encode loop , and hence LPDL ⩽ RPDL, it is shown here that the converse fails. Thus LPDL

Looping vs. repeating in dynamic logic

Following a suggestion of Pratt, we consider propositional dynamic logic in which programs are nondeterministic finite automata over atomic programs and tests (i.e., flowcharts), rather than regular expressions. While the resulting version of PDL, call it APDL, is clearly equivalent in expressive power to PDL, it is also (in the worst case) exponentially more succinct. In particular, deciding its validity problem by reducing it to that of PDL leads to a double exponential time procedure, although PDL itself is decidable in exponential time. We present an elementary combined proof of the completeness of a simple axiom system for APDL and decidability of the validity problem in exponential time. The results are thus stronger than those for PDL, since PDL can be encoded in APDL with no additional cost, and the proofs simpler, since induction on the structure of programs is virtually eliminated. Our axiom system for APDL relates to the PDL system just as Floyd's proof method for partial correctness relates to Hoare's.

Propositional dynamic logic of flowcharts

With the (necessary) condition that atomic programs in process logic (PL) be binary, we present an algorithm for the translation of a PL formula p into a program $\zeta (p)$ of propositional dynamic logic (PDL) such that a finite path satisfies p if it belongs to $\zeta (p)$. This reduction has two immediate corollaries: 1) validity in this PL can be tested by testing validity of formulas in PDL; 2) all state properties expressible in this PL are expressible in PDL. The translation, however, is of nonelementary time complexity.The significance of the result to the search for natural and powerful logics of programs is discussed.

R. Sherman

Papers

STATEMATE: a working environment for the development of complex reactive systems

On the Formal Semantics of Statecharts (Extended Abstract)

Looping vs. repeating in dynamic logic

Propositional dynamic logic of flowcharts

Is the interesting part of process logic uninteresting? A translation from PL to PDL